periodic motions of an impact oscillator abstract non linear equations governing n impact periodic motions of a single degree of freedom oscillator under a sinusoidal and bias force contacting rigid amplitude constraints one or both sides have been developed with constant and velocity dependent coefficients of restitution they also govern period doubling motions additionally exact closed form expressions have been developed for one and two equispaced and non equispaced impacts per cycle motions theoretical predictions agreed with previous results and with results obtained using a numerical simulation approach effects of amplitude and frequency of sinusoidal force bias force damping and variable and constant coefficients of restitution on periodic motions are investigated

the dynamics of repeated impacts with a sinusoidally vibrating table a deceptively simple difference equation is derived which approximately describes the motion of a small ball bouncing vertically on a massive sinusoidally vibrating plate in the case of perfect elastic impacts the equation reduces to the standard mapping which has been extensively studied by physicists in connection with the motions of particles constrained in potential wells it is shown that for sufficiently large excitation velocities and a coefficient of restitution close to one this deterministic dynamical system exhibits large families of irregular non periodic solutions in addition to the expected harmonic and subharmonic motions the physical significance of these and other chaotic motions which appear to occur frequently in non linear oscillations is discussed

applications of the complex interpolation method to a von neumann algebra non commutative lp spaces non commutative lp spaces 1 p associated with a von neumann algebra are considered the paper consists of two parts in part i by making use of the complex interpolation method non commutative lp spaces are defined as interpolation spaces between the von neumann algebra in question and its predual also all expected properties such as duality and uniform convexity are proved in the frame of interpolaton theory and relative modular theory in part ii these lp spaces are compared with haagerup s lp spaces based on this comparison a non commutative analogue of the classical stein weiss interpolation theorem is obtained

spatially inhomogeneous linear inverse problems with possible singularities the objective of the present paper is to introduce the concept of a spatially inhomogeneous linear inverse problem which to the best of the author s knowledge has never been considered previously in statistical framework but is emerging due to a variety of practical applications the special feature of the problem is that the degree of ill posedness depends not only on the scale but also on location in this case the rates of convergence are determined by the interaction of four parameters the smoothness and spatial homogeneity of the unknown function f and degrees of ill posedness and spatial inhomogeneity of operator q an interesting property here is that if operator q is weakly inhomogeneous then the rates of convergence are not influenced by spatial inhomogeneity of operator q and coincide with the rates which are usual for homogeneous linear inverse problems on the other hand if operator q is moderately or strongly inhomogeneous convergence rates are significantly affected by the degree of spatial inhomogeneity estimators obtained in the paper are based either on wavelet vaguelette decomposition if the norms of all vaguelettes are finite or on a hybrid of wavelet vaguelette decomposition and galerkin method if vaguelettes in the neighborhood of the singularity point have infinite norms the hybrid estimator is a combination of a linear part in the vicinity of the singularity point and the nonlinear block thresholding wavelet estimator elsewhere to attain adaptivity an optimal resolution level for the linear singularity affected portion of the estimator is obtained using lepskii 1990 1999 method subsequently this resolution level is used as the lowest resolution level for the nonlinear wavelet estimator we show that convergence rates of the hybrid estimator lie within a logarithmic factor of the optimal minimax convergence rates the theory presented in the paper is supplemented by examples of deconvolution based on irregularly spaced observations or in the presence of a heteroscedastic noise the latter problem is also examined via a limited simulation study which demonstrates advantages of the hybrid estimator when the degree of spatial inhomogeneity is high

adaptive estimation over anisotropic functional classes via oracle approach we address the problem of adaptive minimax estimation in white gaussian noise model under lp loss 1 p 1 on the anisotropic nikolskii classes we present the es timation procedure based on a new data driven selection scheme from the family of kernel estimators with varying bandwidths for proposed estimator we establish so called lp norm oracle inequality and use it for deriving minimax adaptive results we prove the existence of rate adaptive estimators and fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk in particular some new asymptotics of the minimax risk are discovered including necessary and sufficient conditions for existencea uniformly consistent estimator we provide also with detailed overview of existing methods and results and formulate open problems in adaptive minimax estimation

non commutative martingale transforms abstract we prove that non commutative martingale transforms are of weak type 1 1 more precisely there is an absolute constant c such that if m is a semi finite von neumann algebra and m n n 1 is an increasing filtration of von neumann subalgebras of m then for any non commutative martingale x x n n 1 in l 1 m adapted to m n n 1 and any sequence of signs e n n 1 e 1 x 1 n 2 n e n x n x n 1 1 c x n 1 for every n 2 this generalizes a result of burkholder from classical martingale theory to non commutative setting and answers positively a question of pisier and xu as applications we get the optimal order of the unconditional martingale differences umd constants of the schatten class s p when p similarly we prove that the umd constant of the finite dimensional schatten class s n 1 is of order log n 1 we also discuss the pisier xu non commutative burkholder gundy inequalities

experimental observation of nonlinear vibrations in a rub impact rotor system an experimental setup is installed to simulate the rotor to stator rub of the rotor system a special structure of stator is designed that can simulate the condition of the full rub the vibration waveforms spectra orbits and poincare s maps are used to analyze nonlinear responses and bifurcation characteristics of the system when the rub impact occurs experiments with different conditions including one and two rotor with single and multi disks are performed very rich forms of periodic and chaotic vibrations were observed the experiments show that the system motion generally contains the multiple harmonic components such as 2x 3x etc and the 1 2 fractional harmonic components such as 1 2x 3 2x etc under some special conditions the 1 3 fractional harmonic components such as 1 3x 2 3x etc can be observed as well

an inequality in noncommutative lp spaces abstract we prove that for any trace preserving conditional expectation e on a noncommutative l p with p 2 id e is a contraction on the positive cone l p

bayes procedures for adaptive inference in inverse problems for the white noise model we study empirical and hierarchical bayes approaches to the problem of estimating an infinite dimensional parameter in mildly ill posed inverse problems we consider a class of prior distributions indexed by a hyperparameter that quantifies regularity we prove that both methods we consider succeed in automatically selecting this parameter optimally resulting in optimal convergence rates for truths with sobolev or analytic smoothness without using knowledge about this regularity both methods are illustrated by simulation examples

embedding of the operator space oh and the logarithmic little grothendieck inequality we use voiculescu s concept of free probability to construct a completely isomorphic embedding of the operator space oh in the predual of a von neumann algebra we analyze the properties of this embedding and determine the operator space projection constant of oh n frac 1 108 sqrt frac n 1 ln n le inf p mathcal b ell 2 to oh n p 2 p left p right cb le 288 pi sqrt frac 2n 1 ln n the lower estimate is a recent result of pisier and shlyakhtenko that improves an estimate of order 1 1 lnn of the author the additional factor 1 sqrt 1 ln n indicates that the operator space oh n behaves differently than its classical counterpart ell 2 n we give an application of this formula to positive sesquilinear forms on mathcal b ell 2 this leads to logarithmic characterization of c algebras with the weak expectation property introduced by lance

a note on non commutative ergodic theorems for actions of hyperbolic groups abstract the goal of this note is to establish non commutative pointwise ergodic theorems for actions of hyperbolic groups similar commutative results were obtained by bufetov khristoforov and klimenko and by pollicott and sharp

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

forced vibration analysis of a multidegree impact vibrator abstract the dynamics of a multidegree impact vibrator subject to harmonic loading is investigated the system is represented by a lumped mass model which hits and rebounds from a rigid wall during vibration the periodic solution to the equations of motion with n forcing cycles and p impacts is formulated the variational equations and the resulting transition matrix for investigating local stability of the periodic solutions are derived a two degree of freedom example is analysed and a variety of motion types are found chaotic windows are present between regions of periodic response and at these boundaries n p motions are prevalent low velocity impacts are evident at exciting frequencies away from the natural frequencies two basins of attraction are computed and the sensitivity to initial conditions is noted the quality of the n p motion is discussed from an engineering application perspective

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 oracle inequalities related to data driven hard thresholding this paper focuses on computing a nearly optimal penalty in the method of empirical risk minimization it is assumed that we have at our disposal the noisy data y where theta in mathbb r n is an unknown vector and xi in mathbb r n is a standard white gaussian noise it is also assumed that the underling vector is sparse and therefore to recover we use a hard thresholding estimate hat theta i y t y i bf 1 y i ge t in order to adapt to an unknown sparsity of the threshold t is assumed to be data driven the very popular approach for computing such thresholds is based on the principle of empirical risk minimization suggesting the following data driven threshold hat t text arg min t y hat theta y t 2 pen y t where pen y t is a penalty function in this paper it is proved with the help of a sharp oracle inequality that the main term in the optimal penalty is given by 2 2 i yi t log n i yi t

on coverage and local radial rates of credible sets in the mildly ill posed inverse signal in white noise model we construct confidence sets as credible balls with respect to the empirical bayes posterior resulting from a certain two level hierarchical prior the quality of the posterior is characterized by the contraction rate which we allow to be local that is depending on the parameter the issue of optimality of the constructed confidence sets is addressed via a trade off between its size the local radial rate and its coverage probability we introduce excessive bias restriction ebr more general than self similarity and polished tail condition recently studied in the literature under ebr we establish the confidence optimality of our credible set with some local oracle radial rate we also derive the oracle estimation inequality and the oracle posterior contraction rate the obtained local results are more powerful than global adaptive minimax results for a number of smoothness scales follow as consequence in particular the ones considered by szabo et al ann statist 43 2015 1391 1428

the hilbert phenomenon in chaotic motions abstract it is proved that chaotic dynamical systems have d 1 singularity due to such singularity and its periodicity in hausdorff metric spaces a chaotic dynamical system induces a hilbert iterated system which was discovered at the end of the 19th century this implies that the most puzzling discovery in nature in the 20th century can be put into deep correspondence with that in thoughts in the 19th century all this is verified by the numerical experiments of chaotic vibrations of a beam and a tension slack oscillator

sharp adaptation for inverse problems with random noise we consider a heteroscedastic sequence space setup with polynomially increasing variances of observations that allows to treat a number of inverse problems in particular multivariate ones we propose an adaptive estimator that attains simultaneously exact asymptotic minimax constants on every ellipsoid of functions within a wide scale that includes ellipoids with polynomially and exponentially decreasing axes and at the same time satisfies asymptotically exact oracle inequalities within any class of linear estimates having monotone non increasing weights the construction of the estimator is based on a properly penalized blockwise stein s rule with weakly geometically increasing blocks as an application we construct sharp adaptive estimators in the problems of deconvolution and tomography

gundy s decomposition for non commutative martingales and applications we provide an analogue of gundy s decomposition for l 1 bounded non commutative martingales an important difference from the classical case is that for any l 1 bounded non commutative martingale the decomposition consists of four martingales this is strongly related with the row column nature of non commutative hardy spaces of martingales as applications we obtain simpler proofs of the weak type 1 1 boundedness for non commutative martingale transforms and the non commutative analogue of burkholder s weak type inequality for square functions a sequence x n n ge 1 in a normed space mathrm x is called 2 co lacunary if there exists a bounded linear map from the closed linear span of x n n ge 1 to l 2 taking each x n to the n th vector basis of l 2 we prove using our decomposition that any relatively weakly compact martingale difference sequence in l 1 mathcal m tau whose sequence of norms is bounded away from zero is 2 co lacunary generalizing a result of aldous and fremlin to non commutative l 1 spaces

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

on the best constants in noncommutative khintchine type inequalities we obtain new proofs with improved constants of the khintchine type inequality with matrix coefficients in two cases the first case is the pisier and lust piquard noncommutative khintchine inequality for p 1 where we obtain the sharp lower bound of 12 in the complex gaussian case and for the sequence of functions ei2nt n 1 the second case is junge s recent khintchine type inequality for subspaces of the operator space r c which he used to construct a cb embedding of the operator hilbert space oh into the predual of a hyperfinite factor also in this case we obtain a sharp lower bound of 12 as a consequence it follows that any subspace of a quotient of r c is cb isomorphic to a subspace of the predual of the hyperfinite factor of type iii1 with cb isomorphism constant 2 in particular the operator hilbert space oh has this property

on universal oracle inequalities related to high dimensional linear models this paper deals with recovering an unknown vector from the noisy data y a where a is a known m x n matrix and is a white gaussian noise it is assumed that n is large and a may be severely ill posed therefore in order to estimate a spectral regularization method is used and our goal is to choose its regularization parameter with the help of the data y for spectral regularization methods related to the so called ordered smoothers see kneip ann statist 22 1994 835 866 we propose new penalties in the principle of empirical risk minimization the heuristical idea behind these penalties is related to balancing excess risks based on this approach we derive a sharp oracle inequality controlling the mean square risks of data driven spectral regularization methods

lacunary fourier series for compact quantum groups this paper is devoted to the study of sidon sets lambda p sets and some related notions for compact quantum groups we establish several different characterizations of sidon sets and in particular prove that any sidon set in a discrete group is a strong sidon set in the sense of picardello we give several relations between sidon sets lambda p sets and lacunarities for lp fourier multipliers generalizing a previous work by blendek and michalicek we also prove the existence of lambda p sets for orthogonal systems in noncommutative lp spaces and deduce the corresponding properties for compact quantum groups central sidon sets are also discussed and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central sidon sets several examples are also included

ultraproducts qwep von neumann algebras and the effros marechal topology based on the analysis on the ocneanu groh raynaud ultraproducts and the effrosmarechal topology on the space vn h of von neumann algebras acting on a separable hilbert space h we show that for a von neumann algebra m vn h the following conditions are equivalent 1 m has the kirhcberg s quotient weak expectation property qwep 2 m is in the closure of the set finj of injective factors on h with respect to the effros marechal topology 3 m admits an embedding i into the ocneanu ultrapower r of the injective iii1 factor r with a normal faithful conditional expectation e r i m 4 for every e 0 n n and 1 n p m there is k n and a1 an mk c such that i j trk aiaj e 1 i j n holds where trk is the tracial state on mk c and p m is the natural cone in the standard form of m

dilations of semigroups on von neumann algebras and noncommutative lp spaces abstract we prove that any weak continuous semigroup t t t 0 of factorizable markov maps acting on a von neumann algebra m equipped with a normal faithful state can be dilated by a group of markov automorphisms analogous to the case of a single factorizable markov operator which is an optimal result we also give a version of this result for strongly continuous semigroups of operators acting on noncommutative l p spaces and examples of semigroups to which the results of this paper can be applied our results imply the boundedness of the mcintosh s h functional calculus of the generators of these semigroups on the associated noncommutative l p spaces generalising some previous work from junge le merdy and xu finally we also give concrete dilations for poisson semigroups which are even new in the case of r n

the fractal dimension of the two well potential strange attractor abstract the dimension of the duffing holmes two well potential strange attractor has been measured using both numerical solutions and experimental data from chaotic vibrations of a buckled beam using numerical simulation the fractal dimension of the poincare section of the strange attractor has been calculated as a function of damping using a correlation function technique the dimension of the poincare section is between one and two with higher damping resulting in a smaller dimensional attractor an equivalent cantor set for the attractor is defined the dimension seems to be relatively insensitive to the phase of the poincare section an analytical expression for the dimension as a function of damping is proposed the dimension algorithm is applied to experimentally generated poincare maps from chaotic vibrations of a buckled beam the calculation yields a dimension of the poincare map between one and two and seems to be insensitive to the phase of the poincare section

a description of cp lp m rp lp m θ we give a simple explicit description of the norm in the complex interpolation space c p l p m r p l p m for any von neumann algebra m and any 1 p

strongly non linear oscillations of winding machines part i mode locking motion and routes to chaos this study investigates the dynamics of a single degree of freedom sdof wire in a winding machine this system has piecewise linear stiffness and is subjected to a forcing excitation due to imbalance and a parametric excitation due to tension the frequencies of both parametric and forcing excitations are not equal or do not have a ratio of two simple integers using the fourth order runge kutta method and introducing aj integral this strongly non linear system can be estimated for various parameters then the mode locking motions main resonant intervals and subharmonic modes can be found also all possible combined subharmonics and superhamonic motions and routes to chaos are observed byj bifurcation illustrations with the assistance of poincare maps phase portraits response waveforms frequency spectra and lyapunov exponents thus the physical illustrations of such a system can provide stabilization by appropriate design parameters

statistical inverse estimation in hilbert scales the recovery of signals from indirect measurements blurred by random noise is considered under the assumption that prior knowledge regarding the smoothness of the signal is avialable for greater flexibility the general problem is embedded in an abstract hilbert scale in the applications sobolev scales are used for the construction of estimators we employ preconditioning along with regularized operator inversion in the appropriate inner product where the operator is bounded but not necessarily compact a lower bound to certain minimax rates is included and it is shown that in generic examples the proposed estimators attain the asymptotic minimax rate examples include errors in variables deconvolution and indirect nonparametric regression special instances of the latter are estimation of the source term in a differential equation and the estimation of the initial state in the heat equation

grothendieck s theorem for operator spaces we prove several versions of grothendieck s theorem for completely bounded linear maps t e f when e and f are operator spaces we prove that if e f are c algebras of which at least one is exact then every completely bounded t e f can be factorized through the direct sum of the row and column hilbert operator spaces equivalently t can be decomposed as t t r t c where t r resp t c factors completely boundedly through a row resp column hilbert operator space this settles positively at least partially some earlier conjectures of effros ruan and blecher on the factorization of completely bounded bilinear forms on c algebras moreover our result holds more generally for any pair e f of exact operator spaces this yields a characterization of the completely bounded maps from a c algebra or from an exact operator space to the operator hilbert space oh as a corollary we prove that up to a complete isomorphism the row and column hilbert operator spaces and their direct sums are the only operator spaces e such that both e and its dual e are exact we also characterize the schur multipliers which are completely bounded from the space of compact operators to the trace class

an extension of inequalities by ando abstract we give variations on ando s result comparing f b f a and f b a with respect to unitarily invariant norms on matrices

embedding of cq and rq into noncommutative lp spaces 1 p q 2 we prove that a quotient of a subspace of cp prp 1 p 2 embeds completely isomorphically into a noncommutative lp space where cp and rp are respectively the p column and p row hilbertian operator spaces we also represent cq and rq p q 2 as quotients of subspaces of cp prp consequently cq and rq embed completely isomorphically into a noncommutative lp m we further show that the underlying von neumann algebra m cannot be semifinite

bifurcations and chaos in a quasi periodically forced beam theory simulation and experiment abstract non linear vibrations of a straight beam clamped at both ends and forced with two frequencies near the first mode frequency are theoretically and experimentally investigated in an earlier paper the occurrence of chaos in the forced beam was proved by using the galerkin approximation the averaging method and melnikov s technique first the single mode galerkin approximation for the beam is further analyzed here the existence of invariant tori corresponding to periodic orbits in the averaged system is established and their stability is determined the occurrence of saddle node and doubling bifurcations of tori which correspond to saddle node and period doubling bifurcations of periodic orbits in the averaged system respectively is also detected second numerical simulation results for a single mode equation and experimental results for the beam are given the existence of invariant tori and sustained chaotic motions is confirmed and saddle node and doubling bifurcations of tori are observed the bifurcation sets and conditions for the existence of chaos are also obtained these observations in numerical simulations and experiments are compared with the theoretical predictions

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

noncommutative maximal ergodic theorems this paper is devoted to the study of various maximal ergodic theorems in noncommutative spaces in particular we prove the noncommutative analogue of the classical dunford schwartz maximal ergodic inequality for positive contractions on and the analogue of stein s maximal inequality for symmetric positive contractions we also obtain the corresponding individual ergodic theorems we apply these results to a family of natural examples which frequently appear in von neumann algebra theory and in quantum probability

risk bounds for model selection via penalization performance bounds for criteria for model selection are devel oped using recent theory for sieves the model selection criteria are based on an empirical loss or contrast function with an added penalty term moti vated by empirical process theory and roughly proportional to the number of parameters needed to describe the model divided by the number of ob servations most of our examples involve density or regression estimation settings and we focus on the problem of estimating the unknown density or regression function we show that the quadratic risk of the minimum penal ized empirical contrast estimatoris bounded by an index of the accuracy of the sieve this accuracy index quanties the trade off among the candidate models between the approximation error and parameter dimension relative to sample size if we choose a list of models which exhibit good approximation prop erties with respect to different classes of smoothness the estimator can be simultaneously minimax rate optimal in each of those classes this is what is usually called adaptation the type of classes of smoothness in which one gets adaptation depends heavily on the list of models if too many models are involved in order to get accurate approximation of many wide classes of functions simultaneously it may happen that the estimator is only approx

the walsh basis in the lp spaces of hyperfinite iiiλ factors 0 λ 1 abstract we introduce a non commutative walsh system and prove that it forms a schauder basis in the l p spaces 1 p associated with the hyperfinite iii factors 0 1

uniform bounds for norms of sums of independent random functions in this paper we develop a general machinery for finding explicit uniform probability and moment bounds on sub additive positive functionals of random processes using the developed general technique we derive uniform bounds on the ls norms of empirical and regression type processes usefulness of the obtained results is illustrated by application to the processes appearing in kernel density estimation and in nonparametric estimation of regression functions

oracle inequalities for inverse problems we consider a sequence space model of statistical linear inverse problems where we need to estimate a function f from indirect noisy observations let a finite set a of linear estimators be given our aim is to mimic the estimator in a that has the smallest risk on the true f under general conditions we show that this can be achieved by simple minimization of an unbiased risk estimator provided the singular values of the operator of the inverse problem decrease as a power law the main result is a nonasymptotic oracle inequality that is shown to be asymptotically exact this inequality can also be used to obtain sharp minimax adaptive results in particular we apply it to show that minimax adaptation on ellipsoids in the multivariate anisotropic case is realized by minimization of unbiased risk estimator without any loss of efficiency with respect to optimal nonadaptive procedures

global dynamics of a vibro impacting linear oscillator abstract the steady state vibro impacting responses of one dimensional harmonically excited linear oscillators are studied by using a modern dynamical systems approach allied with numerical simulation the steady state motions are attracting sets in the system phase space and capture initial conditions in their domains of attraction unlike the free harmonically excited oscillator the phase space of a vibro impacting system may be inhabited by many attracting sets for example there are sub harmonic multi impact periodic orbits and chaotic steady state responses in order to build a qualitative understanding of vibro impact response an attempt is made to build generic topological models of their phase spaces for physically significant parameter ranges use is made of the poincare section or stroboscopic mapping technique essentially following an initial impact forwards or backwards in time to subsequent or previous impacts using a computer the qualitative understanding gained from the analysis and simulations is discussed in an engineering context

exact solution of stable periodic one contact per n cycles motion of a damped linear oscillator contacting a unilateral elastic stop abstract an exact closed form solution is developed for a damped single degree of freedom oscillator contacting a unilateral stop once per n cycles of external sinusoidal force it also includes the effect of a bias force this solution was obtained by using two different displacement and velocity expressions for a two region piecewise linear oscillator continuity of displacement and velocity at the boundary of the two regions and periodicity conditions contact duration is assumed as known and four simultaneous equations in four unknowns are solved exactly the four unknowns are the amplitude of the sinusoidal force phase angle of the assumed first contact entry velocity and exit velocity of mass the stability of motion is checked using the closed form expressions of elements of a 2 2 stability governing matrix these elements are obtained by considering only first order perturbations in periodic motion theoretical predictions based on exact solution agree with previous results and with results obtained using a numerical simulation approach the relationships are studied in detail between input parameters such as amplitude of external force frequency of external force bias force gap spring stiffness and damping constants and output parameters such as contact duration phase angle at contact entry velocity exit velocity maximum displacement and minimum displacement

les espaces lp d une algebre de von neumann definies par la derivee spatiale abstract this work answers a question raised by a connes on the spatial theory of von neumann algebras preprint inst hautes etudes sci france and generalizes for a general von neumann algebra the theory of non commutative integration of j dixmier bull soc math france 81 1953 and i segal ann of math 57 1973

dynamics of unsymmetric piecewise linear non linear systems using finite elements in time the dynamic response and stability of a single degree of freedom system with unsymmetric piecewise linear non linear stiffness are analyzed using the finite element method in the time domain based on a hamilton s weak principle this method provides a simple and efficient approach for predicting all possible fundamental and sub periodic responses the stability of the steady state response is determined by using floquet s theory without any special effort for calculating transition matrices this method is applied to a number of examples demonstrating its effectiveness even for a strongly non linear problem involving both clearance and continuous stiffness non linearities close agreement is found between available published findings and the predictions of the finite element in time approach which appears to be an efficient and reliable alternative technique for non linear dynamic response and stability analysis of periodic systems

the principle of penalized empirical risk in severely ill posed problems we study a standard method of regularization by projections of the linear inverse problem y ax e where e is a white gaussian noise and a is a known compact operator it is assumed that the eigenvalues of aa converge to zero with exponential decay such behavior of the spectrum is typical for inverse problems related to elliptic differential operators as model example we consider recovering of unknown boundary conditions in the dirichlet problem for the laplace equation on the unit disk by using the singular value decomposition of a we construct a projection estimator of x the bandwidth of this estimator is chosen by a data driven procedure based on the principle of minimization of penalized empirical risk we provide non asymptotic upper bounds for the mean square risk of this method and we show in particular that this approach gives asymptotically minimax estimators in our model example

noncommutative burkholder rosenthal inequalities we investigate martingale inequalities in noncommutative lp spaces associated with a von neumann algebra equipped with a faithful normal state we prove the noncommutative analogue of the classical burkholder inequality on the conditioned or little square function and extend the noncommutative burkholder gundy inequalities from comm math phys 189 1997 667 698 to this nontracial setting we include several related results

rosenthal inequalities in noncommutative symmetric spaces abstract we give a direct proof of the upper khintchine inequality for a noncommutative symmetric quasi banach function space with nontrivial upper boyd index this settles an open question of c le merdy and the fourth named author le merdy and sukochev 2008 24 we apply this result to derive a version of rosenthal s theorem for sums of independent random variables in a noncommutative symmetric space as a result we obtain a new proof of rosenthal s theorem for haagerup l p spaces

stability and bifurcation analysis for oscillators with motion limiting constraints abstract the stability and bifurcation analysis is presented for a class of non linear single degree of freedom vibrating systems excited by harmonic forcing the common characteristic of these systems is that their damping and stiffness parameters can change abruptly at certain displacement values the most general n periodic steady state solutions with an arbitrary number of contacts per response cycle are analyzed it is shown that when the damping is positive the change of stability of the steady state response cannot happen through a hopf bifurcation

conditioned square functions for noncommutative martingales we prove a weak type 1 1 inequality involving conditioned versions of square functions for martingales in noncommutative l p spaces associated with finite von neumann algebras as application we determine the optimal orders for the best constants in the noncommutative burkholder rosenthal inequalities from ann probab 31 2003 948 995 we also discuss bmo norms of sums of noncommuting order independent operators

periodicity of averaged histories of chaotic oscillators abstract this study is dedicated to demonstrate the periodicities embedded in the averaged responses of chaotic systems with periodic excitations recent studies in the field of non linear oscillations often found random like responses for some deterministic non linear systems with periodic excitations which were then named chaotic systems however in this study by discretizing the initial conditions on a chosen domain and averaging the corresponding responses the averaged response can be calculated for the chaotic motions of duffing van der pol and piecewise linear systems these averaged responses exhibit near periodicities with primary frequency components at excitation frequency odd multiples or half multiples of excitation frequency it is also found that this periodicity becomes more evident as the number of discretized initial conditions over a fixed domain these results were obtained and validated by simulations

a reduction method for noncommutative l_p spaces and applications we consider the reduction of problems on general noncommutative l p spaces to the corresponding ones on those associated with finite von neumann algebras the main tool is an unpublished result of the first named author which approximates any noncommutative l p space by tracial ones we show that under some natural conditions a map between two von neumann algebras extends to their crossed products by a locally compact abelian group or to their noncommutative l p spaces we present applications of these results to the theory of noncommutative martingale inequalities by reducing most recent general noncommutative martingale ergodic inequalities to those in the tracial case

observations of invariant structures in the chaotic response of lorenz and other systems a phase plane invariant of the lorenz and other systems undergoing chaos has been presented numerical experiments show that this invariant is independent of the initial conditions and depends on the structure and parameters of the chaotic systems there are some potential applications of this result to the issues of system identification reconstruction of the chaotic systems and chaotic cryptography

a weak type inequality for non commutative martingales and applications we prove a weak type 1 1 inequality for square functions of non commutative martingales that are simultaneously bounded in l 2 and l 1 more precisely the following non commutative analogue of a classical result of burkholder holds there exists an absolute constant k 0 such that if m is a semi finite von neumann algebra and mn 1 1 is an increasing filtration of von neumann subalgebras of m then for any given martingale x xn 1 1 that is bounded in l 2 m l 1 m adapted to mn 1 1 there exist two martingale difference sequences a an 1 1 and b bn 1 1 with dxn an bn for every n 1 1 x n 1 aan 1 2

robust and efficient recovery of a signal passed through a filter and then contaminated by non gaussian noise consider a channel where a continuous periodic input signal is passed through a linear filter and then is contaminated by an additive noise the problem is to recover this signal when we observe n repeated realizations of the output signal adaptive efficient procedures that are asymptotically minimax over all possible procedures are known for channels with gaussian noise and no filter the case of direct observation efficient procedures based on the smoothness of a recovered signal are known for the case of gaussian noise robust rate optimal procedures are known as well however there are no results on robust and efficient data driven procedures moreover the known results for the case of direct observation indicate that even a small deviation from gaussian noise may lead to a drastic change we show that for the considered case of indirect data and a particular class of so called supersmooth filters there exists a procedure of recovery of an input signal that possesses the desired properties namely it is adaptive to the smoothness of the input signal robust to the distribution of the noise globally and pointwise efficient that is its minimax global and pointwise risks converge with the best constant and rate over all possible estimators as n spl rarr spl infin and universal in the sense that for a wide class of linear not necessarily bounded operators the efficient estimator is a plug in one furthermore we explain how to employ the obtained asymptotic results for the practically important case of small n large noise

speed of estimation in positron emission tomography and related inverse problems we study a continuous idealization of the image reconstruction problem in positron emission tomography considered as an example of bivariate density estimation based on indirect observations given a large sample of indirect observations we consider the size of the equivalent sample of observations whose original exact positions would allow equally accurate estimation of the image of interest both for indirect and for direct observations we establish exact minimax rates of convergence of estimation for all possible estimators over suitable smoothness classes of functions the approach of the paper is applicable to a wide class of linear inverse problems

on the optimal rates of convergence for nonparametric deconvolution problems deconvolution problems arise in a variety of situations in statistics an interesting problem is to estimate the density f of a random variable x based on n i i d observations from y x varepsilon where varepsilon is a measurement error with a known distribution in this paper the effect of errors in variables of nonparametric deconvolution is examined insights are gained by showing that the difficulty of deconvolution depends on the smoothness of error distributions the smoother the harder in fact there are two types of optimal rates of convergence according to whether the error distribution is ordinary smooth or supersmooth it is shown that optimal rates of convergence can be achieved by deconvolution kernel density estimators

non periodic motion caused by grazing incidence in an impact oscillator the motion of a single degree of freedom periodically forced oscillator subjected to a rigid amplitude constraint is considered using analytical methods the singularities caused by grazing impact are studied it is shown that as a stable periodic orbit comes to grazing impact under the control of a single parameter a special type of bifurcation occurs the motion after the bifurcation may be non periodic and a criterion for this based on orientation and eigenvalues is given

exact single equation closed form solution of vibrating systems with piecewise linear springs abstract a method is proposed to obtain in a single equation the exact closed form displacement response of both free undamped vibrations and the steady state of forced damped vibrations of systems with piecewise linear springs with continuous or discontinuous force deflection relations since the displacement equations are exact the velocity and acceleration responses are obtained by differentiation the solutions are complete they apply for any value of time from zero to infinity the method is designed to be handled in a computer either in conjunction with a symbolic mathematics package like mathematica or maple or without it however for certain relatively simple problems the phase plane solution may be obtained even in a hand held calculator two examples are presented

risk hull method and regularization by projections of ill posed inverse problems we study a standard method of regularization by projections of the linear inverse problem y af where is a white gaussian noise and a is a known compact operator with singular values converging to zero with polynomial decay the unknown function f is recovered by a projection method using the singular value decomposition of a the bandwidth choice of this projection regularization is governed by a data driven procedure which is based on the principle of risk hull minimization we provide nonasymptotic upper bounds for the mean square risk of this method and we show in particular that in numerical simulations this approach may substantially improve the classical method of unbiased risk estimation

experimental determination of the rubbing location by means of acoustic emission and wavelet transform a method to pinpoint the rubbing location in a rotor bearing system is presented this method is based on the data sampled by acoustic emission ae sensors placed at different bearing supports usually the point where rubbing occurs cannot be detected using the method of cross correlation directly to the data due to the noise produced during rubbing and the structure resonance of the signal through wavelet transform wt signals are decomposed into a series of time domain signals each of which covers a specific octave frequency band then the method of cross correlation is applied to the decomposed signals to detect the rubbing location this method is found to be very effective

non commutative martingale inequalities we prove the analogue of the classical burkholder gundy inequalites for non commutative martingales as applications we give a characterization for an ito clifford integral to be an lp martingale via its integrand and then extend the ito clifford integral theory in l2 developed by barnett streater and wilde to lp for all 1 p we include an appendix on the non commutative analogue of the classical fefferman duality between h1 and bmo

a noncommutative martingale convexity inequality let m be a von neumann algebra equipped with a faithful semifinite normal weight and n be a von neumann subalgebra of m such that the restriction of to n is semifinite and such that n is invariant by the modular group of let e be the weight preserving conditional expectation from m onto n as an application we show that there exists e0 0 such that for any free group fn and any q 4 e0 pt 2 q 1 t logq 1 where pt is the poisson semigroup defined by the natural length function of fn

maurey s factorization theory for operator spaces we prove an operator space version of maurey s theorem which claims that every absolutely p 1 summing map on c k is automatically absolutely q summing for q p our results imply in particular that every completely bounded map from b h with values in pisier s operator space oh is completely p summing for p 2 this fails for p 2 as applications we obtain eigenvalue estimates for translation invariant maps defined on the von neumann algebra vn g associated with a discrete group g we also develop a notion of cotype which is compatible with factorization results on noncommutative lp spaces

the haagerup approximation property for von neumann algebras via quantum markov semigroups and dirichlet forms the haagerup approximation property for a von neumann algebra equipped with a faithful normal state is shown to imply existence of unital preserving and kms symmetric approximating maps this is used to obtain a characterisation of the haagerup approximation property via quantum markov semigroups extending the tracial case result due to jolissaint and martin and further via quantum dirichlet forms

bifurcation and chaos in a rub impact jeffcott rotor system non linear vibration characteristics of a rub impact jeffcott rotor are investigated the system is two dimensional non linear and periodic fourier series analysis and the floquet theory are used to perform qualitative global analysis on bifurcation and stability the governing ordinary differential equations are also integrated using a numerical method to give the quantitative result this preliminary study reveals the chaotic feature of the system after the rub impact as the rotating speed is increased three kinds of routes to chaos are found that is from a stable periodic motion through period doubling bifurcation grazing bifurcation and a sudden transition from periodic motion to chaos quasi periodic motions are also found

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

repeated impacts on a sinusoidally vibrating table reappraised the traditional simplification for one commonly used example of repeated collisions is shown to be frequently erroneous for a wide range of coefficients of restitution bounded errors arise from an artificial speed constraint whose circumvention is largely but not exclusively unpredictable therefore exact equations whose periodic solutions are detailed should be generally used

the periodicity of chaotic impact oscillators in hausdorff phase spaces it is well known that non periodic behavior is one of the most puzzling characteristics of chaotic oscillators so far chaotic dynamical systems have been investigated in euclidean spaces in this paper the concept of non autonomous dynamical systems and that of hausdorff phase spaces are proposed the behavior of chaotic impact oscillators is investigated in hausdorff phase spaces it is discovered that although the non autonomous dynamical systems described by chaotic impact oscillators are non periodic in euclidean phase spaces they are periodic in hausdorff phase spaces this shows that euclidean spaces in which we stayed for hundreds of years may no longer be suitable for the investigation into chaotic phenomena in addition the periodicity of chaotic dynamical systems in hausdorff metric spaces induces a new class of strange invariant sets in euclidean spaces such strange invariant sets may be an ideal symbol of chaotic dynamical systems

more comments on c p we discuss the interpretation of c p plots and show how they can be calibrated in several ways we comment on the practice of using the display as a basis for formal selection of a subset regression model and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients for example ridge estimates