the bishop phelps bollobas version of lindenstrauss properties a and b we study a bishop phelps bollobas version of lindenstrauss properties a and b for domain spaces we study banach spaces x such that x y has the bishopphelps bollobas property bpbp for every banach space y we show that in this case there exists a universal function x e such that for every y the pair x y has the bpbp with this function this allows us to prove some necessary isometric conditions for x to have the property we also prove that if x has this property in every equivalent norm then x is one dimensional for range spaces we study banach spaces y such that x y has the bishop phelps bollobas property for every banach space x in this case we show that there is a universal function y e such that for every x the pair x y has the bpbp with this function this implies that this property of y is strictly stronger than lindenstrauss property b the main tool to get these results is the study of the bishop phelps bollobas property for c0 1and sums of banach spaces

on the modelling of incompressibility in linear and non linear elasticity with the master slave approach this is the pre peer reviewed version of the following article munoz jose j on the modelling of incompressibility in linear and non linear elasticity with the master slave approach international journal for numerical methods in engineering abril 2008 vol 74 num 2 p 269 293 which has been published in final form at http www3 interscience wiley com journal 116323442 abstract

energy consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraints the present work deals with the energy consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraints the underlying differential algebraic equations daes with index three are directly discretized this approach makes possible the development of a new energy consistent time stepping scheme for general nonholonomic systems in particular both nonholonomic problems from rigid body dynamics as well as flexible multibody dynamics can be treated in a unified manner in this connection specific constrained formulations of rigid bodies and geometrically exact beams are presented moreover the newly developed discrete null space method is applied to achieve a size reduction and an improved conditioning of the discrete system the numerical examples deal with a nonholonomic rigid body system and a flexible multibody system

the bishop phelps bollobas theorem for operators we prove the bishop phelps bollobas theorem for operators from an arbitrary banach space x into a banach space y whenever the range space has property of lindenstrauss we also characterize those banach spaces y for which the bishop phelps bollobas theorem holds for operators from 1 into y s everal examples of classes of such spaces are provided for instance the bishop phelps bollobas theorem holds when the range space is finite dimensional an l1 space for a finite measure a c k space for a compact hausdorff space k or a uniformly convex banach space

regularization of higher index differential algebraic equations with rank deficient constraints in this paper we present several regularizations for higher index differential algebraic equations with rank deficient or singular constraints these types of problems arise for example in the solution of constrained mechanical systems when a mechanism s trajectory passes through or near a kinematic singularity we derive a class of regularizations for these problems which is based on minimization of the norm of the constraints the new regularizations are analogous to trust region methods of numerical optimization we give convergence results for the regularizations and present some numerical experiments which illustrate their effectiveness

constrained integration of rigid body dynamics in the present paper rigid body dynamics is formulated as mechanical system with holonomic constraints this approach offers the appealing possibility to deal with finite rotations without employing any specific rotational parameterization the numerical discretization of the underlying system of differential algebraic equations is treated in detail the proposed algorithm obeys major conservation laws of the underlying continuous system such as conservation of energy and angular momentum in addition to that the constraints on the configuration and momentum level are fulfilled exactly two numerical examples are dealt with to assess the performance of the constrained algorithm

modelling unilateral frictionless contact using the null space method and cubic b spline interpolation the analysis of unilateral sliding contact in elasticity is equivalent to a minimisation problem subjected to a set of inequality constraints however the presence of boundary discontinuities such as those stemming from the spatial discretisation appears as a major problem to determine the set of active constraints this work introduces a smoothing technique of the master surface resorting to cubic b spline interpolation which is c 1 continuous in contact situations between elastic and rigid bodies and g 1 continuous in elastic elastic contact problems the technique is applied in conjunction with the null space method where the solution is searched in an unconstrained manifold the resulting formulation eases the contact transition along the master surface and recovers the quadratic convergence of the iterative newton raphson process the robustness of the method is demonstrated using 2d and 3d examples

strongly asymmetric discrete painleve equations the additive case we examine a class of discrete painleve equations which present a strong asymmetry these equations can be written as a system of two equations the right hand sides of which do not have the same functional form we limit here our investigation to two canonical families of the quispel roberts thompson qrt classification both of which lead to difference equations several new integrable discrete systems are identified

on an isomorphic banach mazur rotation problem and maximal norms in banach spaces abstract we prove that the spaces l p 1 p p 2 and all infinite dimensional subspaces of their quotient spaces do not admit equivalent almost transitive renormings this is a step towards the solution of the banach mazur rotation problem which asks whether a separable banach space with a transitive norm has to be isometric or isomorphic to a hilbert space we obtain this as a consequence of a new property of almost transitive spaces with a schauder basis namely we prove that in such spaces the unit vector basis of l 2 2 belongs to the two dimensional asymptotic structure and we obtain some information about the asymptotic structure in higher dimensions further we prove that the spaces l p 1 p p 2 have continuum different renormings with 1 unconditional bases each with a different maximal isometry group and that every symmetric space other than l 2 has at least a countable number of such renormings on the other hand we show that the spaces l p 1 p p 2 have continuum different renormings each with an isometry group which is not contained in any maximal bounded subgroup of the group of isomorphisms of l p

on the numerical solution of the euler lagrange equations the paper presents a new approach to the numerical solution of the euler lagrange equations based upon the reduction of the problem to a second order ordinary differential equation ode on the constraint manifold the algorithm guarantees that the constraints are automatically satisfied and requires a minimal number of evaluations of second order derivative terms in fact second order derivatives are involved only through the second fundamental tensor of the constraint manifold this tensor may be computed either explicitly when second derivatives are available or via an approximation procedure with excellent accuracy examples are given along with comparisons with state of the art software

variational collision integrator for polymer chains the numerical simulation of many particle systems e g in molecular dynamics often involves constraints of various forms we present a symplectic integrator for mechanical systems with holonomic bilateral and unilateral contact constraints the latter being in the form of a non penetration condition the scheme is based on a discrete variant of hamilton s principle in which both the discrete trajectory and the unknown collision time are varied cf r fetecau j marsden m ortiz m west nonsmooth lagrangian mechanics and variational collision integrators siam j appl dyn syst 2 2003 381 416 as a consequence the collision event enters the discrete equations of motion as an unknown that has to be computed on the fly whenever a collision is imminent the additional bilateral constraints are efficiently dealt with employing a discrete null space reduction including a projection and a local reparametrisation step which considerably reduces the number of unknowns and improves the condition number during each time step as compared to a standard treatment with lagrange multipliers we illustrate the numerical scheme with a simple example from polymer dynamics a linear chain of beads and test it against other standard numerical schemes for collision problems

symplectic partitioned runge kutta methods for constrained hamiltonian systems this article deals with the numerical treatment of hamiltonian systems with holonomic constraints a class of partitioned runge kutta methods consisting of the couples of s stage lobatto iiia and lobatto iiib methods has been discovered to solve these problems efficiently these methods are symplectic preserve all un derlying constraints and are superconvergent with order 2s 2 for separable hamiltonians of the form h q p frac 1 2 p t m 1 p u q the rattle algorithm based on the verlet method was up to now the only known symplectic method preserving the constraints in fact this method turns out to be equivalent to the 2 stage lobatto iiia iiib method of order 2 numerical examples have been performed which illustrate the theoretical results

galerkin lie group variational integrators based on unit quaternion interpolation abstract lie group variational integrators of arbitrary order are developed using the galerkin method based on unit quaternion interpolation to our knowledge quaternions have not been used before for this purpose though they allow a very simple and efficient way to perform the interpolation the resulting integrators are symplectic and structure preserving in the sense that certain symmetries in the lagrangian of the mechanical system are carried over to the discrete setting which leads to the preservation of the corresponding momentum maps the integrators furthermore exhibit a very good long time energy behavior i e energy is neither dissipated nor gained artificially at the same time the lie group structure is preserved by carefully defining the variations the interpolation method and by solving the non linear system of equations directly on the manifold rather than constraining it in a surrounding space using lagrange multipliers as a consequence we are able to show that lie group variational integrators based on the special orthogonal group are equivalent to the variational integrators for constrained systems using the discrete null space method employed e g in dmocc discrete mechanics and optimal control of constrained systems we show new numerical results on the convergence rates which are substantially higher than the known theoretical bounds and on the relation between accuracy and computational cost

a new formulation for the direct dynamic simulation of flexible mechanisms based on the newton euler inverse method this paper is concerned with the direct dynamic analysis of mechanisms comprising flexible members it is first recalled how the time integration of the dynamic equations governing the motion of a flexible mechanism is conditioned by the availability of the so called iteration matrix the latter is obtained not only from the mass matrix which is sufficient in the rigid case but also from the stiffness and damping tangent matrices hence in a context based upon relative co ordinates where the deformation of the flexible bodies is described by component modes two formulations a classical one and a new one which permit the determination of this iteration matrix are presented the classical formulation is based upon the lagrange s theorem the new one consists in a direct calculation of the residues of the dynamic equations by using the inverse method of newton euler in this case the iteration matrix is obtained by a numerical derivation technique which proves well conditioned a first simple example is treated in order to compare the two formulations a more complex one illustrates the real capabilities of the new formulation

mechanical systems subject to holonomic constraints differential algebraic formulations and conservative integration abstract the numerical integration in time of the equations of motion for mechanical systems subject to holonomic constraints is considered schemes are introduced for the direct treatment of a differential algebraic form of the equations that preserve the constraints the total energy and other integrals such as linear and angular momentum arising from affine symmetries moreover the schemes can be shown to preserve the property of time reversibility in an appropriate sense an example is given to illustrate various aspects of the proposed methods

constraint preserving integrators for general nonlinear higher index daes in the last few years there has been considerable research on numerical methods for differential algebraic equations daes f x x t 0 where f x is identically singular the index provides one measure of the singularity of a dae most of the numerical analysis literature on daes to date has dealt with daes with indices no larger than three even in this case the systems were often assumed to have a special structure recently a numerical method was proposed that could in principle be used to integrate general unstructured higher index solvable daes however that method did not preserve constraints this paper will discuss a modification of that approach which can be used to design constraint preserving integrators for general nonlinear higher index daes

numerical solution of differential algebraic equations in mechanical systems simulation abstract the numerical solution of the differential algebraic equations of motion of mechanical systems offers many computational challenges in this paper we describe progress which has been made in understanding the formulation of the equations of motion from the viewpoint of numerical stability and outline some of the difficulties which must be resolved for efficient and reliable numerical methods in real time simulation of mechanical systems

bishop phelps bollobas property for certain spaces of operators abstract we characterize the banach spaces y for which certain subspaces of operators from l 1 into y have the bishop phelps bollobas property in terms of a geometric property of y namely ahsp this characterization applies to the spaces of compact and weakly compact operators new examples of banach spaces y with ahsp are provided we also obtain that certain ideals of asplund operators satisfy the bishop phelps bollobas property

discontinuous variational time integrators for complex multibody collisions the objective of the present work is to formulate a new class of discontinuous variational time integrators that allow the system to adopt two possibly different configurations at each sampling time tk representing predictor and corrector configurations of the system the resulting sequence of configuration pairs then represents a discontinuous or non classical trajectory continuous or classical trajectories are recovered simply by enforcing a continuity constraint at all times in particular in systems subject to one sided contact constraints simulated via discontinuous variational time integrators the predictor configuration is not required to satisfy the one sided constraints whereas the corrector configuration is obtained by a closest point projection cpp onto the admissible set the resulting trajectories are generally discontinuous or non classical but are expected to converge to classical or continuous solutions for decreasing time steps we account for dissipation including friction by means of a discrete lagrange d alembert principle and make extensive use of the spacetime formalism in order to ensure exact energy conservation in conservative systems and the right rate of energy decay in dissipative systems the structure range and scope of the discontinuous variational time integrators and their accuracy characteristics are illustrated by means of examples of application concerned with rigid multibody dynamics

a mortar approach for fluid structure interaction problems immersed strategies for deformable and rigid bodies abstract this paper proposes a new fluid structure interaction immersed computational framework the coupling between an underlying incompressible fluid and an embedded solid is formulated by means of the overlapping domain decomposition method in conjunction with a mortar approach leading to a variationally consistent scheme which is capable of unifying a range of methodologies currently available in the literature this novel framework provides great flexibility and enables the modelling of immersed deformable solids compressible and incompressible as well as rigid bodies through the use of a weak director based formulation a novel null space reduction scheme is employed in order to enhance the conditioning of the resulting system of equations and reduce the computational cost an implicit structure preserving time integration algorithm is used to yield extra stability and robustness and the use of a segmentation technique near the boundary between fluid and solid also leads to enhanced accuracy the methodology is benchmarked against results obtained by using alternative boundary fitted methodologies

efficient numerical solution of constrained multibody dynamics systems abstract a numerical algorithm for conducting coupled system dynamical simulation is presented the interconnected system comprising numerous modules is treated as a constrained multibody dynamics system of particular focus is the efficient solution of coupled system simulation without sacrificing the independence of the separate dynamical modules the proposed algorithm maggi s equations with perturbed iteration mepi emanates from numerical methods for differential algebraic equations separate treatment of the constraint equations from the resolution of subsystem dynamical responses marks mepi s main characteristic

the bishop phelps bollobas theorem fails for bilinear forms on l1 l1 abstract in this paper we show that the bishop phelps bollobas theorem fails for bilinear forms on l 1 l 1 while it holds for linear operators from l 1 to l

locally uniformly rotund points in convex transitive banach spaces abstract almost transitive superreflexive banach spaces have been considered in c finet uniform convexity properties of norms on superreflexive banach spaces israel j math 53 1986 81 92 where it is shown that they are uniformly convex and uniformly smooth we characterize such spaces as those convex transitive banach spaces satisfying conditions much weaker than that of uniform convexity for example that of having a weakly locally uniformly rotund point we note that in general the property of convex transitivity for a banach space is weaker than that of almost transitivity

discrete variational lie group formulation of geometrically exact beam dynamics the goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics by using a lie group variational integrator both spatial and temporal discretization are implemented in a geometry preserving manner the resulting scheme preserves both the discrete momentum maps and symplectic structures and exhibits almost perfect energy conservation comparisons with existing numerical schemes are provided and the convergence behavior is analyzed numerically

the bishop phelps bollobas theorem for l l1 μ l 0 1 abstract we show that the bishop phelps bollobas theorem holds for all bounded operators from l 1 into l 0 1 where is a finite measure

manpak a set of algorithms for computations on implicitly defined manifolds abstract mathematical models often involve differentiable manifolds that are implicitly defined as the solution sets of systems of nonlinear equations the resulting computational tasks differ considerably from those arising for manifolds defined in parametric form here a collection of algorithms is presented for performing a range of essential tasks on general implicitly specified submanifolds of a finite dimensional space this includes algorithms for determining local parametrizations and their derivatives and for evaluating quantities related to the curvature with sensitivity measures the methods have been implemented as a fortran 77 package called manpak

real time integration methods for mechanical system simulation this study focuses on the mechanical system dynamics applications of differential algebraic equations dae selected papers develop the foundations of dae as they appear in mechanical system dynamics applications and explore the foundations of contemporary methods for the numerical solution of dae in mechanical system dynamics many theoretical methods and methods of generalized co ordinate partitioning for the numerical integration of dae are examined the text has been designed to encompass a broad range of applications in engineering and applied physics

a time integration algorithm for flexible mechanism dynamics the dae α method this paper introduces a new family of second order methods for solving the index 2 differential algebraic equations daes of motion for flexible mechanism dynamics these methods which extend the methods for odes of structural dynamics to daes possess numerical dissipation that can be controlled by the user convergence and stability analysis is given and verifies that the dae methods introduce no additional oscillations and preserve the stability of the underlying ode system convergence of the newton iteration which can be a source of difficulty in solving nonlinear oscillatory systems with large stepsizes is achieved via a coordinate split modification to the newton iteration numerical results illustrate the effectiveness of the new methods for simulation of flexible mechanisms

banach spaces with a large semigroup of contractive automorphisms abstract transitivity almost transitivity and convex transitivity are classical notions in the isometric theory of banach spaces all of them related to mazur s problem asking whether transitive separable banach spaces are hilbert spaces 24 33 in this paper we study near versions of the above notions roughly speaking nearness means that contractive automorphisms play the role played by surjective linear isometries in the corresponding classical notion we also consider asymptotic transitivity as defined in 35 which is implied by almost transitivity and implies near almost transitivity and introduce the corresponding notion of asymptotic convex transitivity we show that nearly convex transitive respectively asymptotically convex transitive banach spaces are nearly almost transitive respectively asymptotically transitive uniformly smooth and uniformly convex as soon as they be asplund spaces or have the radon nikod m property we also deal with a property stronger than the near transitivity and weaker than the uniform micro semitransitivity 18 we prove that banach spaces with this intermediate property are uniformly smooth and uniformly convex finally we show that nearly almost transitive norm unital complete normed possibly non associative algebras are hilbert spaces

self duality and schlesinger chains for the asymmetric d pii and q piii equations we analyse two asymmetric discrete painleve equations namely d pii and q piii which are known to be discrete forms of piii and pvi respectively we show that both equations are self dual this means that the same equation governs the evolution along the discrete independent variable and the transformations under the action of the schlesinger transforms along the parameters of the discrete painleve a bilinear formulation of the self dual equation is given as a system of nonautonomous hirota miwa equations

conservation properties of a time fe method part iii mechanical systems with holonomic constraints a galerkin based discretization method for index 3 differential algebraic equations pertaining to finite dimensional mechanical systems with holonomic constraints is proposed in particular the mixed galerkin mg methodis introduced which leads in a natural way to time stepping schemes that inherit major conservation properties of the underlying constrained hamiltonian system namely total energy and angular momentum in addition to that the constraints on the configuration level and on the velocity momentum level are fulfilled exactly the application of the mg method to specific mechanical systems such as the pendulum rigid body dynamics and the coupled motion of rigid and flexible bodies is presented related numerical examples are investigated to evaluate the numerical performance of the mg 1 and mg 2 method

direct determination of periodic solutions of the dynamical equations of flexible mechanisms and manipulators a method based on finite elements characterized by generalized strains as functions of the nodal co ordinates is the basis for the computer program spacar for the kinematic and dynamic analysis of flexible multibody systems this program allows also the evaluation of the linearized dynamical equations which makes possible the implementation of a method for the direct determination of stationary and periodic solutions and of a continuation method for these solutions if some parameter is varied as an illustration these methods are applied to a duffing equation a double pendulum and a slider crank mechanism with an elastic connecting rod

an orthonormal tangent space method for constrained multibody systems abstract an automatic computer code for constructing an orthonormal basis of tangent null space for constrained multibody systems is proposed the method uses the gram schmidt vector orthogonalization process adjusted to the riemannian geometry formalism an important and useful peculiarity of the formulation is that the minimal order purely differential equations of the constrained motion are obtained directly in the resolved form i e the mass matrix of the equations is the unity matrix some other interesting features of the formulation leading to additional gain in efficiency of the dynamic analysis of constrained systems are also reported

rigid body dynamics in terms of quaternions hamiltonian formulation and conserving numerical integration in the present paper unit quaternions are used to describe the rotational motion of a rigid body the unit length constraint is enforced explicitly by means of an algebraic constraint correspondingly the equations of motion assume the form of differential algebraic equations daes a new route to the derivation of the mass matrix associated with the quaternion formulation is presented in contrast to previous works the newly proposed approach yields a non singular mass matrix consequently the passage to the hamiltonian framework is made possible without the need to introduce undetermined inertia terms the hamiltonian form of the daes along with the notion of a discrete derivative make possible the design of a new quaternion based energy momentum scheme two numerical examples demonstrate the performance of the newly developed method in this connection comparison is made with a quaternion based variational integrator a director based energy momentum scheme and a momentum conserving scheme relying on the discretization of the classical euler s equations

rational surfaces associated with affine root systems and geometry of the painleve equations we present a geometric approach to the theory of painleve equations based on rational surfaces our starting point is a compact smooth rational surface x which has a unique anti canonical divisor d of canonical type we classify all such surfaces x to each x there corresponds a root subsystem of e 1 8 inside the picard lattice of x we realize the action of the corresponding affine weyl group as the cremona action on a family of these surfaces we show that the translation part of the affine weyl group gives rise to discrete painleve equations and that the above action constitutes their group of symmetries by backlund transformations the six painleve differential equations appear as degenerate cases of this construction in the latter context x is okamoto s space of initial conditions and d is the pole divisor of the symplectic form defining the hamiltonian structure

a mortar method for energy momentum conserving schemes in frictionless dynamic contact problems summary in the present work the mortar method is applied to planar large deformation contact problems without friction in particular the proposed form of the mortar contact constraints is invariant under translations and rotations these invariance properties lay the foundation for the design of energy momentum timestepping schemes for contact impact problems the iterative solution procedure is embedded into an active set algorithm lagrange multipliers are used to enforce the mortar contact constraints the solution of generalized saddle point systems is circumvented by applying the discrete null space method numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energymomentum scheme copyright q 2008 john wiley sons ltd

from continuous to discrete painleve equations abstract discrete analogues of the painleve equations have recently been derived using either a method based on orthogonal polynomials or the singularity confinement method here we analyze additional methods for deriving integrable non autonomous discrete equations these methods are based on the discrete akns approach on the use of backlund and schlesinger transforms of the continuous painleve equations and on discrete analogues of miura transformations

new contiguity relation of the sixth painleve equation from a truncation for the master painleve equation p6 u we define a consistent method adapted from the weiss truncation for partial differential equations which allows us to obtain the first degree birational transformation of okamoto two new features are implemented to achieve this result the first one is the homography between the derivative of the solution u and a riccati pseudopotential the second one is an improvement of a conjecture by fokas and ablowitz on the structure of this birational transformation we then build the contiguity relation of p6 which yields one new second order non autonomous discrete equation

least squares completions for nonlinear differential algebraic equations a method has been proposed for numerically solving lower dimensional nonlinear higher index differential algebraic equations for which more classical methods such as backward differentiation or implicit runge kutta may not be appropriate this method is based on solving nonlinear dae derivative arrays using nonlinear singular least squares methods the theoretical foundations generality and limitations of this approach remain to be determined this paper carefully examines several key aspects of this approach the emphasis is on general results rather than specific results based on the structure of various applications

symplectic numerical integrators in constrained hamiltonian systems recent work reported in the literature suggests that for the long time integration of hamiltonian dynamical systems one should use methods that preserve the symplectic or canonical structure of the flow here we investigate the symplecticness of numerical integrators for constrained dynamics such as occur in molecular dynamics when bond lengths are made rigid in order to overcome stepsize limitations due to the highest frequencies this leads to a constrained hamiltonian system of smaller dimension previous work has shown that it is possible to have methods which are symplectic on the constraint manifold in phase space here it is shown that the very popular verlet method with shake type constraints is equivalent to the same method with rattle type constraints and that the latter is symplectic and time reversible this assumes that the iteration is carried to convergence we also demonstrate the global convergence of the verlet scheme in the presence of shake type and rattle type constraints we perform numerical experiments to compare these methods with the second order backward differentiation method commonly recommended for ordinary differential equations with constraints

discrete systems related to the sixth painleve equation we present discrete painleve equations which can be obtained as contiguity relations of the solutions of the continuous painleve vi the derivation is based on the geometry of the affine weyl group d 1 4 associated with the bilinear formalism as an offshoot we also present the contiguity relations of the solutions of the bureau ablowitz fokas equation which is a miura transformed modified pvi

a discrete mechanics approach to the cosserat rod theory part 1 static equilibria a theory of discrete cosserat rods is formulated in the language of discrete lagrangian mechanics by exploiting kirchhoff s kinetic analogy the potential energy density of a rod is a function on the tangent bundle of the configuration manifold and thus formally corresponds to the lagrangian function of a dynamical system the equilibrium equations are derived from a variational principle using a formulation that involves null space matrices in this formulation no lagrange multipliers are necessary to enforce orthonormality of the directors noether s theorem relates first integrals of the equilibrium equations to lie group actions on the configuration bundle so called symmetries the symmetries relevant for rod mechanics are frame indifference isotropy and uniformity we show that a completely analogous and self contained theory of discrete rods can be formulated in which the arc length is a discrete variable ab initio in this formulation the potential energy density is defined directly on pairs of points along the arc length of the rod in analogy to veselov s discrete reformulation of lagrangian mechanics a discrete version of noether s theorem then identifies exact first integrals of the discrete equilibrium equations these exact conservation properties confer the discrete solutions accuracy and robustness as demonstrated by selected examples of application

the bishop phelps bollobas property and lush spaces abstract we prove that for every lush space x the couple l 1 x has the bishop phelps bollobas property for operators that is every lush space has the ahsp standing for the approximate hyperplane series property while every lush space has the alternative daugavet property there exists a space with the alternative daugavet property that does not have the ahsp we also show that there is a banach space with both the ahsp and the alternative daugavet property which is not lush

on banach spaces whose group of isometries acts micro transitively on the unit sphere abstract we study banach spaces whose group of isometries acts micro transitively on the unit sphere we introduce a weaker property inherited by one complemented subspaces that we call uniform micro semitransitivity we prove a number of results about both micro transitive and uniformly micro semitransitive spaces in particular they are uniformly convex and uniformly smooth and form a self dual class to this end we relate the fact that the group of isometries acts micro transitively with a property of operators called the pointwise bishop phelps bollobas property and use some known results on it besides we show that if there is a non hilbertian non separable banach space with uniform micro semitransitive or micro transitive norm then there is a non hilbertian separable one finally we show that an l p space is micro transitive or uniformly micro semitransitive only when p 2

on isometry groups and maximal symmetry we study problems of maximal symmetry in banach spaces this is done by providing an analysis of the structure of small subgroups of the general linear group gl x where x is a separable reflexive banach space in particular we provide the first known example of a banach space x without any equivalent maximal norm or equivalently such that gl x contains no maximal bounded subgroup moreover this space x may be chosen to be super reflexive in memory of greg hjorth 1963 2011 and nigel kalton 1946 2010

optimization and differentiation in banach spaces abstract we show that some old ideas of smulian can be used to give another proof of a theorem of bourgain we characterize subsets of banach spaces having the radon nikodym property by means of optimization results

on a unified approach to transformations and elementary solutions of painleve equations an algorithmic method is developed for investigating the transformation properties of second order equations of painleve type this method which utilizes the singularity structure of these equations yields explicit transformations which relate solutions of the painleve equations ii vi with different parameters these transformations easily generate rational and other elementary solutions of the equations the relationship between painleve equations and certain new equations quadratic in the second derivative of painleve type is also discussed

the discrete null space method for the energy consistent integration of constrained mechanical systems part ii multibody dynamics summary in the present work rigid bodies and multibody systems are regarded as constrained mechanical systems at the outset the constraints may be divided into two classes i internal constraints which are intimately connected with the assumption of rigidity of the bodies and ii external constraints related to the presence of joints in a multibody framework concerning external constraints lower kinematic pairs such as revolute and prismatic pairs are treated in detail both internal and external constraints are dealt with on an equal footing the present approach thus circumvents the use of rotational variables throughout the whole time discretization after the discretization has been completed a size reduction of the discrete system is performed by eliminating the constraint forces in the wake of the size reduction potential conditioning problems are eliminated the newly proposed methodology facilitates the design of energy momentum methods for multibody dynamics the numerical examples deal with a gyro top cylindrical and planar pairs and a six body linkage copyright 2006 john wiley sons ltd

on the use of geometrically exact shells in a conserving framework for flexible multibody dynamics abstract the present work deals with the design of energy momentum conserving schemes for flexible multibody dynamics the proposed approach is based on nonlinear finite element methods for the space discretization of flexible bodies in particular the focus is on geometrically exact shells relying on reissner mindlin kinematics it is shown that the equations of motion pertaining to the semi discrete shell formulation can be written in the form of differential algebraic equations daes the daes provide a uniform framework for a rotationless description of flexible multibody dynamics the use of rotational parameters is circumvented throughout the discretization process in space and time the rotationless description facilitates the straightforward incorporation of geometrically exact shells and beams into a multibody framework in addition to that the advocated approach makes possible the design of a uniform energy momentum conserving time stepping scheme for general multibody systems numerical examples demonstrate the excellent numerical stability properties of the present scheme moreover comparison is made with more traditional formulations based on rotational parameters

an ergodic sampling scheme for constrained hamiltonian systems with applications to molecular dynamics this article addresses the problem of computing the gibbs distribu tion of a hamiltonian system that is subject to holonomic constraints in doing so we extend recent ideas of cances et al m2an vol 41 no 2 pp 351 389 2007 who could prove a law of large numbers for unconstrained molecular systems with a separable hamiltonian em ploying a discrete version of hamilton s principle studying ergodicity for constrained hamiltonian systems we specifically focus on the numerical discretization error even if the continuous system is perfectly ergodic this property is typically not preserved by the numerical discretization the discretization error is taken care of by means of a hybrid monte carlo al gorithm that allows for sampling bias free expectation values with respect to the gibbs measure independently of the stable step size we give a demonstration of the sampling algorithm by calculating the free energy profile of a small peptide

the bishop phelps bollobas property for operators between spaces of continuous functions abstract we show that the space of bounded linear operators between spaces of continuous functions on compact hausdorff topological spaces has the bishop phelps bollobas property a similar result is also proved for the class of compact operators from the space of continuous functions vanishing at infinity on a locally compact and hausdorff topological space into a uniformly convex space and for the class of compact operators from a banach space into a predual of an l 1 space

a discrete momentum conserving explicit algorithm for rigid body dynamics analysis a discrete momentum conserving explicit time integration is presented the accurate feature and simplicity of the present algorithm are realized by a mid point implicit formula for integrating the euler parameters and a second order discrete momentum conserving form of the central difference algorithm respectively the accuracy and robustness of the algorithm is demonstrated by example problems which exhibit large overall rigid motions under holonomic constraints

conservative rigid body dynamics by convected base vectors with implicit constraints abstract a conservative time integration formulation is developed for rigid bodies based on a convected set of orthonormal base vectors the base vectors are represented in terms of their absolute coordinates and thus the formulation makes use of three translation components plus nine components of the base vectors orthogonality and unit length of the base vectors are imposed by constraining the equivalent green strain components and the kinetic energy is represented corresponding to rigid body motion the equations of motion are obtained via hamilton s equations including the zero strain conditions as well as external constraints via lagrange multipliers subsequently the lagrange multipliers associated with the internal zero strain constraints are eliminated by use of a set of orthogonality conditions between the generalized displacements and the momentum vector leaving a set of differential equations without additional algebraic constraints on the base vectors a discretized form of the equations of motion is obtained by starting from a finite time increment of the hamiltonian and retracing the steps of the continuous formulation in discrete form in terms of increments and mean values over each integration time increment in this discrete form the lagrange multipliers are given in terms of a representative value within the integration time interval and the equations of motion are recast into a conservative mean value and finite difference format the lagrange multipliers are eliminated explicitly within each integration interval leaving a projection operator expressed in terms of displacement component mean values hereby the number of variables is reduced by six for each rigid body in the problem and the difference equations lead to conservation of the orthonormality conditions for the local base vectors examples demonstrate the efficiency and accuracy of the procedure

the discrete null space method for the energy consistent integration of constrained mechanical systems part i holonomic constraints the present work deals with energy consistent time stepping schemes for finite dimensional mechanical systems with holonomic constraints the proposed procedure is essentially based upon the following steps firstly the index three differential algebraic equations corresponding to the constrained mechanical system are directly discretized secondly the discrete lagrange multipliers are eliminated by using a discrete null space matrix in many cases it is feasible to further reduce the number of unknowns by employing specific reparametrizations the proposed method entails a number of advantageous features such as size reduction and improved conditioning of the resulting system of algebraic equations it is shown that the newly developed method is well suited for both open loop and closed loop multibody systems