the non linear equations of motion of pipes conveying fluid abstract the non linear equations of motion of pipes conveying fluid are derived in simple and accessible terms by energy and newtonian methods different derivations are made for cantilevered pipes where the centreline is assumed inextensible and for pipes with both ends fixed it is shown that the derivations the origin of the various terms and the structure of the equations are distinctly different in these two cases the equations of motion are then compared with those already in existence e g by holmes rousselet and herrmann and lundgren sethna and bajaj at the same time clarifying the derivations and assumptions made and discussing the validity and completeness of the final equations some of the equations are found to be fully correct indeed superior to those derived here while others are found to be deficient because of assumptions made or inconsistencies in the derivations for pipes with both ends fixed the equations given in this paper are considered to be the most complete and correct

vibration and stability of a cracked translating beam abstract the vibration and stability characteristics of a cracked beam translating between fixed supports are investigated using hamilton s principle and elementary fracture mechanics the equations of motion for the beam are developed throughout this analysis it is assumed that the crack is shallow and always remains open i e crack closure and the associated impact conditions are not considered in order to restrict attention to the open crack scenario parameter regimes corresponding to 1 a fully open crack 2 a fully closed crack and 3 a partly open partly closed crack are clearly identified for parameter values in regime 1 the free vibration characteristics are studied via an eigenanalysis this shows that the natural frequencies im and stability characteristics re fluctuate as the crack translates along with the beam between the two supports for the shallow cracks being considered the fluctuations are attributed primarily to the localized drop in the mass per unit length occurring at the crack rather than from the increased flexibility furthermore the magnitudes of these fluctuations are shown to vary with both the axial transport speed and the crack depth and are mapped in the control parameter space implications for the free and forced vibration problems are discussed

analysis of additive dependencies and concurvities using smallest additive principal components additive principal components are a nonlinear generalization of linear principal components their distinguishing feature is that linear forms i a i x i are replaced with additive functions i f i x i a considerable amount of flexibility for fitting data is gained when linear methods are replaced with additive ones our interest is in the smallest principal components which is somewhat uncommon smallest additive principal components amount to data descriptions in terms of approximate implicit equations i f i x i 0 estimation of such equations is a data analytic method in its own right competing in some cases with the more customary regression approaches it is also a diagnostic tool in additive regression for detection of so called concurvity this term describes degeneracies among predictor variables in additive regression models similar to collinearity in linear regression models concurvity may lead to statistically unstable contributions of variables to additive models as an example we show in a reanalysis of the ozone data from breiman and friedman that concurvity does indeed exist in this particular data a fact which may impact the interpretation of the additive fits in the second half of this paper we give some second order theory including the description of null situations and eigenexpansions derived from associated eigenproblems we show how ace and additive principal components are related and we outline some analytical methods for theoretical calculations of additive principal components lastly we consider methods of estimation and computation additive principal components have had a long tradition in psychometric research and correspondence analysis they have started receiving attention by statisticians only in recent years

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

systemes dynamiques non commutatifs et moyennabilite on introduit la notion de fonction de type positif relativement a un systeme dynamique c dont les proprietes sont analogues a celles des fonctions de type positif classiques on montre que dans le cas d un groupe discret g agissant sur une algebre de von neumann m la moyennabilite de l action est equivalente a l existence d une suite bornee de fonctions de type positif sur g a support fini a valeurs dans le centre z m de m qui converge vers 1 pour la topologie de la convergence simple ultrafaible

fe analysis of a moving beam using lagrangian multiplier method lagrangian multiplier technique is employed to develop a h p version finite element model for a certain class of dynamics problems legendre polynomials are used as shape functions owing to its orthogonality property variational principle is the basis of this formulation with essential conditions applied via lagrangian multipliers the example considered here is a problem of a beam moving over supports response behavior of the beam is investigated for various longitudinal motions the present finite element model is validated by comparing the results with previous research work lagrangian multiplier implementation of the problem with finite element technique is very effective compared to other global methods such as assumed mode technique the inconsistencies in the model presented by lee 1993 are also pointed out

dynamic characteristics and mode localization of elastically constrained axially moving strings and beams abstract the free vibration response of an axially moving string and euler bernoulli beam supported by an intermediate elastic constraint is studied the transfer function method is used to formulate the free response solution for the beam the elastic constraint can consist of either a transverse spring or both transverse and rotational springs the effects of both speed and tension on mode localization are studied a wave analysis is employed to further investigate the behaviour of the systems reflection and transmission coefficients are formulated to show the effects of the system parameters on the coupling of the subsystems the addition of the constraint is shown to increase the critical speed of the beam for low values of tension for the string mode localization increases as speed increases however the behaviour of the beam is shown to change significantly depending on both the system parameters and type of constraint the effects of tension and speed on the delocalization frequency of the weakly bi coupled beam are also presented

vibrations of an axially accelerating beam with small flexural stiffness transverse vibrations of an axially moving beam are considered the axial velocity is harmonically varying about a mean velocity the equation of motion is expressed in terms of dimensionless quantities the beam effects are assumed to be small since in this case the fourth order spatial derivative multiplies a small parameter the mathematical model becomes a boundary layer type of problem approximate solutions are searched using the method of multiple scales and the method of matched asymptotic expansions results of both methods are contrasted with the outer solution

spectral analysis for the transverse vibration of an axially moving timoshenko beam the use of frequency dependent spectral element matrix or exact dynamic stiffness matrix in structural dynamics is known to provide very accurate solutions while reducing the number of degrees of freedom to resolve the computational and cost problems thus in the present paper the spectral element model is formulated for the axially moving timoshenko beam under a uniform axial tension the high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions the effects of the axial velocity and axial tension on the vibration characteristics the dispersion relation and the stability of a moving timoshenko beam are analytically and numerically investigated

supercritical stability of an axially moving beam part i model and equilibrium analysis axially moving material problems consider the dynamic response vibration and stability of long slender members which are in a state of translation this study focuses on the response of axially moving beam like elements at translation speeds that exceed the classical critical speed stability limit a non linear model for an axially moving beam is derived that accounts for the initial beam curvature induced by supporting pulleys or wheels presently the model is used to determine steady responses at critical and supercritical translation speeds the properties of the equilibrium problem are examined using an approximate linear solution and an exact non linear solution the deficiency of the linear solution is illustrated by its inability to capture essential features of the equilibrium problem particularly near and above the critical speed in this high speed region the translating beam undergoes large overall buckling deformations leading to multiple and bifurcated equilibrium states the stability of the equilibria is assessed in part ii

approximation properties for group algebras and group von neumann algebras let g be a locally compact group let c g resp vn g be the c algebra resp the von neumann algebra associated with the left regular representation i of g let a g be the fourier algebra of g and let moa g be the set of completely bounded multipliers of a g with the completely bounded norm moa g is a dual space and we say that g has the approximation property ap if there is a net ua of functions in a g with compact support such that ua a 1 in the associated weak topology in particular g has the ap if g is weakly amenable a g has an approximate identity that is bounded in the completely bounded norm for a discrete group f we show that f has the ap x c f has the slice map property for subspaces of any c algebra x vn jt has the slice map property for a weakly closed subspaces of any von neumann algebra property se the semidirect product of weakly amenable groups need not be weakly amenable we show that the larger class of groups with the ap is stable with respect to semidirect products and more generally this class is stable with respect to group extensions we also obtain some results concerning crossed products for example we show that the crossed product m a g of a von neumann algebra m with property s by a group g with the ap also has property s

exactness of locally compact groups we give some new characterizations of exactness for locally compact second countable groups in particular we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact hausdorff space this answers an open question by anantharaman delaroche

ghostbusting and property a abstract we show that the roe algebra of a bounded geometry metric space contains non compact ghosts if and only if the space does not have property a

wave propagation in and vibration of a travelling beam with and without non linear effects part i free vibration the relation between the wave propagation and the free vibration in a travelling beam with simple supports has been thoroughly investigated the frequency equation of such a beam has been derived using the phase closure principle since the characters of the waves change drastically as the axial speed is increased beyond a certain value the phase closure principle has been applied differently in these two speed regimes the justifications for some approximate methods of obtaining the natural frequencies are also discussed lastly the non linear normal modes are derived again using the phase closure principle the computation of the forced response using the wave propagation approach is discussed in part ii

c operator systems and crossed products abstract the purpose of this paper is to introduce a consistent notion of universal and reduced crossed products by actions and coactions of groups on operator systems and operator spaces in particular we shall put emphasis to reveal the full power of the universal properties of the universal crossed products it turns out to make things consistent one has to perform the constructions in some bigger categories which allow the right framework for studying the universal properties and which are stable under the construction of crossed products even for non discrete groups in the case of operator systems this larger category is what we call a c operator system i e a selfadjoint subspace x of some b h which contains a c algebra a such that a x x x a in the case of operator spaces the larger category is given by what we call c operator bimodules we introduce the notion of crossed products in these categories and show that the classical imai takai and katayama duality theorems for crossed products by group co actions on c algebras extend to our notion of crossed products by c operator systems and c operator bimodules

vibrations of an axially moving beam with time dependent velocity the dynamic response of an axially accelerating elastic tensioned beam is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity these systems experience a coriolis acceleration component which renders such systems gyroscopic the equation of motion is solved by using perturbation analysis principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for different flexural stiffness values and for the first two modes

the slice map problem and approximation properties we show that a weakly closed subspace j of the bounded operators bh on an infinite dimensional hilbert space h has property s the fubini product lt l for all weakly closed subspaces t b h if and only if j satisfies a certain approximation property which we call the weak approximation property the weak approximation property is implied by but does not imply the weak completely bounded approximation property moreover if j has the weak approximation property then the predual j has the approximation property for banach spaces we also prove analagous results for property s and variations of property s for c algebras as an application of our characterization of subspaces with property s we show that the reflexive algebra tensor product formula alg l1 alg l2 alg l1 l2 is not always valid in fact we show that for each of the types ii1 ii and iii 0 1 there is a separably acting factor m alg l1 of that type and a reflexive algebra a alg l2 such that alg l1 alg l2 is strictly contained in alg l1 l2

rigidity for von neumann algebras given by locally compact groups and their crossed products we prove the first rigidity and classification theorems for crossed product von neumann algebras given by actions of non discrete locally compact groups we prove that for arbitrary free probability measure preserving actions of connected simple lie groups of real rank one the crossed product has a unique cartan subalgebra up to unitary conjugacy we then deduce a w strong rigidity theorem for irreducible actions of products of such groups more generally our results hold for products of locally compact groups that are nonamenable weakly amenable and that belong to ozawa s class mathcal s

amenability and exactness for dynamical systems and their c algebras we study the relations between amenability resp amenability at infinity of c dynamical systems and equality or nuclearity resp exactness of the corresponding crossed products

dynamics of a beam moving over multiple supports abstract the equations of motion of a beam moving over multiple supports are formulated based on hamilton s principle and the assumed mode method the supports are either roller supports which impart motion to the beam or frictionless supports with the beam being pushed or pulled over them in both cases the supports are regarded as very stiff springs acting on the moving beam a feature of the present formulation is that its complexity does not increase with an increased number of supports results of numerical simulations are presented for various prescribed motions of the beam

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

on the boundary conditions for axially moving beams axially moving beam typed structures are of technical importance and present in a wide class of engineering problem as the axial speed of a beam may significantly affect the dynamic characteristics of the structure even at a low velocity it is important to accurately predict the dynamic characteristics and stability of such structures in most previous studies the net energy flux through the left end and right end boundaries of the finite beam over two simple supports has been implicitly assumed to be zero by completely ignoring the effects of its left incoming and right outgoing semi infinite beam parts or by applying fixed boundary conditions for its longitudinal vibration which seems to be very non realistic from the physical point of view thus this paper investigates the effects of the continuously incoming and outgoing semi infinite beam parts on the dynamic characteristics and stability of an axially moving beam by using the spectral element method the spectral element model is formulated from the equations of motion derived by using the hamilton s principle extended for the systems of changing mass it is numerically shown that the effects of the continuously incoming and outgoing semi infinite beam parts should be taken into account for further accurate prediction of the dynamic characteristics and stability for such axially moving beams