analysis of a zig zag array of circular inclusions in a solid under uniaxial tension abstract this paper is concerned with a theoretical analysis of an infinite zig zag array of circular inclusions in an infinite solid under uniaxial tension we take properly defined unit regions assume the complex stress potentials to he in the form of laurent and taylor series expansions and determine the unknown coefficients from the boundary conditions for the unit regions numerical results for the interface stresses and the effect of inclusions on the tensile stiffness of the solid are given for various combinations of the mechanical and geometric parameters the results are fitted to reliable polynomial formulac for the convenience of engineering applications

selected problems of frequency analysis for time varying discrete time systems using singular value decomposition and discrete fourier transform the paper develops tools and methods for linear time varying discrete time systems analysis it consists of two parts the first one gives a theoretical background there are definitions and numerical algorithms for approximating frequency characteristics the main method is based on singular value decomposition discrete fourier transform and power density spectrum approach the second part of the paper contains numerical examples six different models have been analyzed three for frequency characteristics approximation and the other three for evaluating the degree of system non stationarity some of the models are time variant and some are time invariant for better evaluation results yielded by the proposed method are compared with classical bode characteristics

ζ function and heat kernel formulae abstract we present a systematic study of asymptotic behaviour of generalised functions and heat kernels used in noncommutative geometry and clarify their connections with dixmier traces we strengthen and complete a number of results from the recent literature and answer in the affirmative the question raised by m benameur and t fack 2006 1

subspace identification of bilinear and lpv systems for open and closed loop data in this paper we present a novel algorithm to identify lpv systems with affine parameter dependence operating under open and closed loop conditions a factorization is introduced which makes it possible to form a predictor that predicts the output which is based on past inputs outputs and scheduling data the predictor contains the lpv equivalent of the markov parameters using this predictor ideas from closed loop lti identification are developed to estimate the state sequence from which the lpv system matrices can be constructed a numerically efficient implementation is presented using the kernel method it turns out that if structure is present in the scheduling sequence the computational complexity reduces even more

recursive functional series modeling estimators for identification of time varying plants more bad news than good the properties of a class of recursive estimators the exponentially weighted functional series modeling estimators are discussed these estimators can be used e g in adaptive prediction or control applications it is argued that there exists a relationship between the amount of information about time varying system parameters which is available a priori and the robustness of the identification algorithm based on such prior knowledge the more specialized the estimation algorithm is the less reliable it might be under nonstandard conditions this is the reason why simple algorithms such as exponentially weighted least squares have to be recommended as if no information about the system nonstationarity is available in advance

a wavelet based approach for the identification of linear time varying dynamical systems a novel procedure is developed for the identification of linear discrete models of dynamical systems from noisy data of particular interest is the application of the methodology to time varying systems the procedure is based on a representation of the governing differential equations with respect to a wavelet basis and the formulation of an inverse algebraic problem in the associated subspace the effect of noisy data is considered and numerical simulations demonstrating the applicability of the method to single and multi degree of freedom dynamical systems are presented

modal identification based on gaussian continuous time autoregressive moving average model a new time domain modal identification method of the linear time invariant system driven by the non stationary gaussian random force is presented in this paper the proposed technique is based on the multivariate continuous time autoregressive moving average carma model this method can identify physical parameters of a system from the response only data to do this we first transform the structural dynamic equation into the carma model and subsequently rewrite it in the state space form second we present the exact maximum likelihood estimators of parameters of the continuous time autoregressive car model by virtue of the girsanov theorem under the assumption that the uniformly modulated function is approximately equal to a constant matrix over a very short period of time then based on the relation between the car model and the carma model we present the exact maximum likelihood estimators of parameters of the carma model finally the modal parameters are identified by the eigenvalue analysis method numerical results show that the method we introduced here not only has high precision and robustness but also has very high computing efficiency therefore it is suitable for real time modal identification

the zeta function of the laplacian on certain fractals we prove that the zeta function of the laplacian a on self similar fractals with spectral decimation admits a meromorphic continuation to the whole complex plane we characterise the poles compute their residues and give expressions for some special values of the zeta function furthermore we discuss the presence of oscillations in the eigenvalue counting function thereby answering a question posed by j kigami and m lapidus for this class of fractals

time frequency formulation design and implementation of time varying optimal filters for signal estimation this paper presents a time frequency framework for optimal linear filters signal estimators in nonstationary environments we develop time frequency formulations for the optimal linear filter time varying wiener filter and the optimal linear time varying filter under a projection side constraint these time frequency formulations extend the simple and intuitive spectral representations that are valid in the stationary case to the practically important case of underspread nonstationary processes furthermore we propose an approximate time frequency design of both optimal filters and we present bounds that show that for underspread processes the time frequency designed filters are nearly optimal we also introduce extended filter design schemes using a weighted error criterion and we discuss an efficient time frequency implementation of optimal filters using multiwindow short time fourier transforms our theoretical results are illustrated by numerical simulations

time frequency arma models and parameter estimators for underspread nonstationary random processes parsimonious parametric models for nonstationary random processes are useful in many applications here we consider a nonstationary extension of the classical autoregressive moving average arma model that we term the time frequency autoregressive moving average tfarma model this model uses frequency shifts in addition to time shifts delays for modeling nonstationary process dynamics the tfarma model and its special cases the tfar and tfma models are shown to be specific types of time varying arma ar ma models they are attractive because of their parsimony for underspread processes that is nonstationary processes with a limited time frequency correlation structure we develop computationally efficient order recursive estimators for the tfarma tfar and tfma model parameters which are based on linear time frequency yule walker equations or on a new time frequency cepstrum simulation results demonstrate that the proposed parameter estimators outperform existing estimators for time varying arma ar ma models with respect to accuracy and or numerical efficiency an application to the time varying spectral analysis of a natural signal is also discussed

fully symmetric functionals on a marcinkiewicz space are dixmier traces abstract as a consequence of the exposition of dixmier type traces in the book of a connes 1994 2 we were led to ask how general is this class of functionals within the space of all unitarily invariant functionals on the corresponding marcinkiewicz ideal m in this paper we prove the surprising result that the set of all dixmier traces on m coincides with the set of all fully symmetric functionals on this space

dixmier traces and extrapolation description of noncommutative lorentz spaces we study the connections between dixmier traces functions and traces of heat semigroups beyond the dual of the macaev ideal and in the general context of semifinite von neumann algebras we show that the correct framework for this investigation is that of operator lorentz spaces possessing an extrapolation description we demonstrate the applicability of our results to hormander weyl pseudo differential calculus on rn in this context we prove that the dixmier trace of a pseudo differential operator coincides with the dixmier integral of its symbol

dixmier measurability in marcinkiewicz spaces and applications abstract we present new results concerning the description of dixmier measurable elements in the sense of a connes in marcinkiewicz spaces and demonstrate some applications of our results in particular we complement famous connes trace theorem by describing the asymptotics of the singular function of order n classical pseudo differential operators on an n dimensional compact riemannian manifold

eigenvalue estimates and mutual information for the linear time varying channel we consider linear time varying channels with additive white gaussian noise for a large class of such channels we derive rigorous estimates of the eigenvalues of the correlation matrix of the effective channel in terms of the sampled time varying transfer function and thus provide a theoretical justification for a relationship that has been frequently observed in the literature we then use this eigenvalue estimate to derive an estimate of the mutual information of the channel our approach is constructive and is based on a careful balance of the tradeoff between approximate operator diagonalization signal dimension loss and accuracy of eigenvalue estimates

spectral flow and dixmier traces abstract we obtain general theorems which enable the calculation of the dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semi finite von neumann algebra our results have several applications we deduce a formula for the chern character of an odd l 1 summable breuer fredholm module in terms of a hochschild 1 cycle we explain how to derive a wodzicki residue for pseudo differential operators along the orbits of an ergodic r n action on a compact space x finally we give a short proof of an index theorem of lesch for generalised toeplitz operators

measures from dixmier traces and zeta functions for l functions on a closed compact riemannian manifold the noncommutative residue and the dixmier trace formulation of the noncommutative integral are shown to equate to a multiple of the lebesgue integral the identifications are shown to continue to and be sharp at l2 functions for functions strictly in lp 1 p 2 symmetrised noncommutative residue and dixmier trace formulas must be introduced for which the identification is shown to continue for the noncommutative residue however a failure is shown for the dixmier trace formulation at l1 functions it is shown the noncommutative residue remains finite and recovers the lebesgue integral for any integrable function while the dixmier trace expression can diverge the results show that a claim in the monograph j m gracia bondia j c varilly h figueroa elements of noncommutative geometry birkhauser adv texts birkhauser boston 2001 that the equality on c functions between the lebesgue integral and an operator theoretic expression involving a dixmier trace obtained from connes trace theorem can be extended to any integrable function is false the results of this paper include a general presentation for finitely generated von neumann algebras of commuting bounded operators including a bounded borel or l functional calculus version of c results in iv 2 of a connes noncommutative geometry academic press new york 1994

on the transfer function calculus for underspread ltv channels the freedom in the definition of a time varying transfer function is formalized by introducing the generalized weyl correspondence which includes zadeh s 1950 function and the weyl symbol for slowly time varying linear systems with properly limited memory underspread ltv systems we prove the asymptotic validity of the multiplicative transfer function calculus

the dixmier trace and asymptotics of zeta functions abstract we obtain general theorems which enable the calculation of the dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup we prove our results in a general semi finite von neumann algebra we find for p 1 that the asymptotics of the zeta function determines an ideal strictly larger than l p on which the dixmier trace may be defined we also establish stronger versions of other results on dixmier traces and zeta functions

invariant banach limits and applications let l be the space of all bounded sequences x x1 x2 with the norm x l supn xn and let l l be the set of all bounded linear operators on l we present a set of easily verifiable sufficient conditions on an operator h l l guaranteeing the existence of a banach limit b on l such that b bh we apply our results to the classical cesaro operator c on l and give necessary and sufficient condition for an element x l to have fixed value bx for all cesaro invariant banach limits b finally we apply the preceding description to obtain a characterization of measurable elements from the dixmier macaev sargent ideal of compact operators with respect to an important subclass of dixmier traces generated by all cesaro invariant banach limits it is shown that this class is strictly larger than the class of all measurable elements with respect to the class of all dixmier traces

identification of linear time varying mdof dynamic systems from forced excitation using hilbert transform and emd method an algorithm is developed for the identification of linear time varying ltv multiple degrees of freedom systems it is based on the hilbert transform and the empirical mode decomposition with forced vibration response data the proposed identification algorithm is applied to single degree of freedom and multi degrees of freedom dynamic systems three ideal cases of ltv systems with smoothly varying abruptly varying and periodically varying stiffness and damping are studied to illustrate the capability of the algorithm to track the variations of the system simulation results demonstrate the effectiveness and the robustness of the proposed identification algorithm and the lack of complete orthogonality for any two intrinsic mode functions is one of the sources of error in the identification

a dixmier trace formula for the density of states a version of connes trace formula allows to associate a measure on the essential spectrum of a schrodinger operator with bounded potential in solid state physics there is another celebrated measure associated with such operators the density of states in this paper we demonstrate that these two measures coincide we show how this equality can be used to give explicit formulae for the density of states in some circumstances

maximum likelihood estimator of operational modal analysis for linear time varying structures in time frequency domain abstract this paper investigates the problem of modal parameter estimation of time varying structures under unknown excitation a time frequency domain maximum likelihood estimator of modal parameters for linear time varying structures is presented by adapting the frequency domain maximum likelihood estimator to the time frequency domain the proposed estimator is parametric that is the linear time varying structures are represented by a time dependent common denominator model to adapt the existing frequency domain estimator for time invariant structures to the time frequency methods for time varying cases an orthogonal polynomial and z domain mapping hybrid basis function is presented which has the advantageous numerical condition and with which it is convenient to calculate the modal parameters a series of numerical examples have evaluated and illustrated the performance of the proposed maximum likelihood estimator and a group of laboratory experiments has further validated the proposed estimator

realization and identification of autonomous linear periodically time varying systems abstract the subsampling of a linear periodically time varying system results in a collection of linear time invariant systems with common poles this key fact known as lifting is used in a two step realization method the first step is the realization of the time invariant dynamics the lifted system computationally this step is a rank revealing factorization of a block hankel matrix the second step derives a state space representation of the periodic time varying system it is shown that no extra computations are required in the second step the computational complexity of the overall method is therefore equal to the complexity for the realization of the lifted system a modification of the realization method is proposed which makes the complexity independent of the parameter variation period replacing the rank revealing factorization in the realization algorithm by structured low rank approximation yields a maximum likelihood identification method existing methods for structured low rank approximation are used to identify efficiently a linear periodically time varying system these methods can deal with missing data

the action functional in non commutative geometry we establish the equality between the restriction of the adler manin wodzicki residue or non commutative residue to pseudodifferential operators of order n on ann dimensional compact manifoldm with the trace which j dixmier constructed on the macaev ideal we then use the latter trace to recover the yang mills interaction in the context of non commutative differential geometry

nonstationary spectral analysis based on time frequency operator symbols and underspread approximations we present a unified framework for time varying or time frequency tf spectra of nonstationary random processes in terms of tf operator symbols we provide axiomatic definitions and tf operator symbol formulations for two broad classes of tf spectra one of which is new these classes contain all major existing tf spectra such as the wigner ville evolutionary instantaneous power and physical spectrum our subsequent analysis focuses on the practically important case of nonstationary processes with negligible high lag tf correlations so called underspread processes we demonstrate that for underspread processes all tf spectra yield effectively identical results and satisfy several desirable properties at least approximately we also show that gabor frames provide approximate karhunen loeve kl functions of underspread processes and tf spectra provide a corresponding approximate kl spectrum finally we formulate simple approximate input output relations for the tf spectra of underspread processes that are passed through underspread linear time varying systems all approximations are substantiated mathematically by upper bounds on the associated approximation errors our results establish a tf calculus for the second order analysis and time varying filtering of underspread processes that is as simple as the conventional spectral calculus for stationary processes

fubini theorem in noncommutative geometry abstract we discuss the fubini formula in alain connes noncommutative geometry we present a sufficient condition on spectral triples for which a fubini formula holds true the condition is natural and related to heat semigroup asymptotics we provide examples of spectral triples for which the fubini formula fails

on the general treatment of multiple inclusions in antiplane elastostatics this article provides an explicit general solution of an infinitely extended plate containing any number of circular inclusions under antiplane deformation the derived solution of the present heterogeneous problem associated with multiple inclusions is obtained in terms of the corresponding homogeneous solution by a simple algebraic substitution this is accomplished by the technique of analytical continuation and the method of successive approximations a rapidly convergent series solution either in the matrix or in the inclusions which is expressed in terms of an explicit general term involving the complex potential of the corresponding homogeneous problem is derived in an elegant form the present derived solution can also be applied to the inclusion problem with straight boundaries numerical examples of three circular inclusions embedded in an infinite matrix in a half plane matrix and in a strip are discussed in detail and displayed in graphic form interaction of a crack with multiple circular inclusions is also considered

on the problem of linear elasticity for an infinite region containing a finite number of non intersecting spherical inhomogeneities abstract the problem of linear elasticity for an infinite number of non intersecting spherical and more generally ellipsoidal inhomogeneities is attacked the approach taken does not misrepresent geometry of inhomogeneities although the continuity conditions at the intefaces are only approximately satisfied the principal idea of the approach is to extend the method of kachanov 1985 int j fracture28 r11 r19 1987 int j solids structures23 23 43 for interacting cracks to the realm of the eshelby equivalent inclusion method the application to a test problem for two spherical cavities suggests that the approach can be useful for predictions of the overall response of composite materials and interfacial stress concentrations

time frequency transfer function calculus symbolic calculus of linear time varying systems linear operators based on a generalized underspread theory we introduce a generalized concept of underspread linear time varying systems linear operators which contains a previous definition as a special case we show that an existing approximate transfer function calculus symbolic calculus can be extended to this wider and practically more relevant class of underspread operators as a mathematical underpinning of this calculus we establish explicit bounds on various error quantities associated with it the transfer function calculus provides a theoretical basis for various methods recently proposed for nonstationary signal processing and it has important implications in the theory of time varying power spectra

traces of compact operators and the noncommutative residue abstract we extend the noncommutative residue of m wodzicki on compactly supported classical pseudo differential operators of order d and generalise a connes trace theorem which states that the residue can be calculated using a singular trace on compact operators contrary to the role of the noncommutative residue for the classical pseudo differential operators a corollary is that the pseudo differential operators of order d do not have a unique trace pseudo differential operators can be non measurable in connes sense other corollaries are given clarifying the role of dixmier traces in noncommutative geometry including the definitive statement of connes original theorem

boundary integral equations for notch problems in plane thermoelasticity where re and im denote the real and imaginary parts of the brack eted expression respectively the quantities qx andqy in eq 2 are the components of heatux in the x and y directions respectively and k is the heat conductivity consider a remote uniform heatux approachedfromthenegative x axisobstructedbythepresenceofan insulated notch or hole in an in nite medium the current problem can be treated as a sum of the corresponding in nite medium prob lem without notches and a corrective term the solution associated with the former problem can be easily expressed as q0 z qim z 3 with q being the strength of heatux applied at in nity on the other hand a corrective solution associated with an in nite medium with a single notch can be obtained by assuming a continuousdistribution of dislocationswith thedensity b0 s placed along a given contour l as h z i i 2p l log z i t b

sampling and reconstruction of operators we study the recovery of operators with a bandlimited kohn nirenberg symbol from the action of such operators on a weighted impulse train a procedure we refer to as sampling of operators kailath bello and later kozek and the authors have shown that the sampling of operators is possible if the symbol of the operator is bandlimited to a set with area less than one in this paper we develop the theory of the sampling of operators in analogy with the classical theory of sampling of bandlimited functions we define the notions of sampling set and sampling rate for operators and give necessary and sufficient conditions on the sampling rate that depend on the size and geometry of the bandlimiting set we develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions we give necessary and sufficient conditions on the bandlimiting set under which sampling of operators is possible by their action on a given periodically weighted delta train we show that under mild geometric conditions on the bandlimiting set classes of operators are bandlimited to an unknown set of area less than one half permit sampling and reconstruction we generalize two results of the heckel and bolcskei concerning sampling of operators with area not greater than one half and less than one respectively by finding a larger class of operators to which they apply operators with bandlimited symbols have been used to model doubly dispersive communication channels with slowly time varying impulse response the results in this paper are rooted in work by bello and kailath in the 1960s

measurable operators and the asymptotics of heat kernels and zeta functions abstract in this note we answer some questions inspired by the introduction in connes 1988 1994 6 7 of the notion of measurable operators using dixmier traces these questions concern the relationship of measurability to the asymptotics of functions and heat kernels the answers have remained elusive for some 15 years

dixmier traces and residues on weak operator ideals we develop the theory of modulated operators in general principal ideals of compact operators for laplacian modulated operators we establish connes trace formula in its local euclidean model and a global version thereof it expresses dixmier traces in terms of the vector valued wodzicki residue we demonstrate the applicability of our main results in the context of log classical pseudo differential operators studied by lesch and a class of operators naturally appearing in noncommutative geometry c 2020 elsevier inc all rights reserved

singular traces and perturbation formulae of higher order abstract let h v be self adjoint operators such that v belongs to the weak trace class ideal we prove higher order perturbation formula f h v j 0 n 1 1 j d j d t j f h t v t 0 r f n t d m n t where is a trace on the weak trace class ideal and m n is a finite measure that is not necessarily absolutely continuous this result extends the first and second order perturbation formulas of dykema and shripka who generalised the krein and koplienko trace formulas to the weak trace class ideal we also establish the perturbation formulae when the perturbation v belongs to the quasi banach ideal weak l n for any n 1

extension of modal analysis to linear time varying systems linear time varying ltv systems have been often dealt with on a case by case basis many well developed concepts and analytic methods of linear time invariant lti systems cannot be applied to ltv systems for example the conventional definition of modal parameters is invalid for ltv systems the first part of this paper explores the possibility of extending the modal concept of ltv systems the discrete time state space model is used to represent ltv systems by analogy to lti systems the pseudo modal parameters are defined using the eigenvalues of the discrete time state transition matrix the paper shows that the pseudo modal parameters preserve certain properties of the conventional modal parameters defined for lti systems the second part of the paper extends a previously developed algorithm to identify the pseudo modal parameters using forced responses and forcing inputs for a general ltv system the input and output hankel matrices formed by an ensemble of data satisfy a matrix facotrization relation the key step of the method is to modify the output matrix in such a way that the range space of the observability matrix can be extracted a robotic manipulator with varying inertia links is used as an example the first part of the numerical simulation illustrates the applications of the pseudo modal parameters the second part of the simulation tests the identification algorithm under different conditions several practical issues are addressed

type ii non commutative geometry i dixmier trace in von neumann algebras abstract we define the notion of connes von neumann spectral triple and consider the associated index problem we compute the analytic chern connes character of such a generalized spectral triple and prove the corresponding local formula for its hochschild class this formula involves the dixmier trace for ii von neumann algebras in the case of foliations we identify this dixmier trace with the corresponding measured wodzicki residue

integration on locally compact noncommutative spaces abstract we present an ab initio approach to integration theory for nonunital spectral triples this is done without reference to local units and in the full generality of semifinite noncommutative geometry the main result is an equality between the dixmier trace and generalised residue of the zeta function and heat kernel of suitable operators we also examine definitions for integrable bounded elements of a spectral triple based on zeta function heat kernel and dixmier trace techniques we show that zeta functions and heat kernels yield equivalent notions of integrability which imply dixmier traceability

interaction between a crack and a circular elastic inclusion under remote uniform heat flow abstract the plane interaction problem for a circular elastic inclusion embedded in an elastic matrix with an arbitrarily oriented crack located either in the matrix or in the inclusion under remote uniform heat flow is considered by using the complex variable theory and the existing solutions for dislocation functions the thermoelastic problem of a crack in the form of an arbitrary shape in the vicinity of the interface is formulated the integral equations for a line crack are then obtained as a system of singular integral equations with logarithmic singular kernels the stress intensity factors which can properly reflect the interaction between a crack and a circular inclusion are obtained in terms of the values of the density functions of the integral equations several numerical examples are given to demonstrate the effects of geometrical parameters and material property combinations on the strength of the thermal stress singularity

system identification and model reduction for a single link flexible manipulator a new model reduction and updating technique is proposed and applied in modelling of a single link flexible manipulator the observability range space extraction algorithm is used to generate an initial overparameterized state space model the identified model is transformed into modal realization the modal responses of individual modes are evaluated a new measure is proposed to quantify the contribution of individual modes to the total responses using the proposed measure a reduced order model is obtained by retaining the most significant modes to improve model accuracy either the reduced input or output matrix can be recalculated by a proposed method several critical issues related to the experimental identification are addressed experimental identification results are presented to illustrate the proposed technique

invariant linear functionals on l r abstract we consider a continuous version of the classical notion of banach limits i e normalized positive linear functionals on l r invariant under translations f x f x s of l r for every s 0 we give one of its characterizations in terms of the invariance under the operation of a certain linear transformation on l r we also deal with invariant linear functionals under dilations f x f r x r 1 and give a similar characterization via the hardy operator applications to summability methods are presented in the last section

dixmier traces as singular symmetric functionals and applications to measurable operators abstract we unify various constructions and contribute to the theory of singular symmetric functionals on marcinkiewicz function operator spaces this affords a new approach to the non normal dixmier and connes dixmier traces introduced by dixmier and adapted to non commutative geometry by connes living on a general marcinkiewicz space associated with an arbitrary semifinite von neumann algebra the corollaries to our approach stated in terms of the operator ideal l 1 which is a special example of an operator marcinkiewicz space are i a new characterization of the set of all positive measurable operators from l 1 i e those on which an arbitrary connes dixmier trace yields the same value in the special case when the operator ideal l 1 is considered on a type i infinite factor a bounded operator x belongs to l 1 if and only if the sequence of singular numbers s n x n 1 in the descending order and counting the multiplicities satisfies x 1 sup n 1 1 log 1 n n 1 n s n x in this case our characterization amounts to saying that a positive element x l 1 is measurable if and only if lim n 1 log n n 1 n s n x exists ii the set of dixmier traces and the set of connes dixmier traces are norming sets up to equivalence for the space l 1 l 0 1 where the space l 0 1 is the closure of all finite rank operators in l 1 in the norm 1

wideband weyl symbols for dispersive time varying processing of systems and random signals we extend the narrowband weyl symbol ws and the wideband p sub o weyl symbol pows for dispersive time frequency tf analysis of nonstationary random processes and time varying systems we obtain the new tf symbols using unitary transformations on the ws and the p sub o ws for example whereas the ws is matched to systems with constant or linear tf characteristics the new symbols are better matched to systems with dispersive nonlinear tf structures this results from matching the geometry of the unitary transformation to the specific tf characteristics of a system we also develop new classes of smoothed weyl symbols that are covariant to tf shifts or time shift and scaling system transformations these classes of symbols are also extended via unitary warpings to obtain classes of tf symbols covariant to dispersive shifts we provide examples of the new symbols and symbol classes and we list some of their desirable properties using simulation examples we demonstrate the advantage of using tf symbols that are matched to the changes in the tf characteristics of a system or random process we also provide new tf formulations for matched detection applications

thermoelastic interaction between a hole and an elastic circular inclusion the plane interaction problem for a circular elastic inclusion with an arbitrarily oriented hole located either in the matrix or in the inclusion under a remote uniform heat flow is solved the proposed method is based on the complex variable theory and the existing solutions for dislocation functions which permit us to formulate boundary integral equations with a weak singular kernel the unknown coefficients left in the singular integral equations thus can be solved numerically by applying the appropriate interpolation formulas the hoop stresses which are directly related to the coefficients of dislocation functions are then determined accordingly several numerical examples are given to demonstrate the use of the present approach comparisons between the calculated numerical results and the corresponding existing solutions show that the method proposed is effective simple and general

transient heat conduction in a medium with multiple circular cavities and inhomogeneities summary a two dimensional transient heat conduction problem of multiple interacting circular inhomogeneities cavities and point sources is considered in general a non perfect contact at the matrix inhomogeneity interfaces is assumed with the heat flux through the interface proportional to the temperature jump the approach is based on the use of the general solutions to the problems of a single cavity and an inhomogeneity and superposition application of the laplace transform and the so called addition theorem results in an analytical transformed solution the solution in the time domain is obtained by performing a numerical inversion of the laplace transform several numerical examples are given to demonstrate the accuracy and the efficiency of the method the approximation error decreases exponentially with the number of the degrees of freedom in the problem a comparison of the companion two and threedimensional problems demonstrates the effect of the dimensionality copyright q 2009 john wiley sons ltd

solutions of thermoelastic crack problems in bonded dissimilar media or half plane medium the two dimensional thermoelastic crack problem in bonded dissimilar media or in a half plane medium is considered the proposed method for solving this problem consists of two parts in the first part complex potential functions are derived which are enforced to satisfy the continuity conditions across the interface while the second part consists of the derivation of singular integral equations by introducing the dislocation functions along the crack border which are solved numerically for both half plane and two bonded half plane problems associated with an insulated crack the thermal stress intensity factors are computed numerically by using the appropriate interpolation formulae the results compared with those of the homogeneous case given in the literature show that the method proposed here is effective simple and general

response of linear slowly varying systems under external excitations abstract an approximate closed form solution for a linear slowly varying system under external excitation is derived the derivation of the solution is based on the technique of freezing slowly varying parameters a technique used in establishing the stability of slowly varying homogeneous systems the error between the approximate and exact solutions is given and an upper bound on the norm of the error in terms of a measure of the rate of change of the system matrix and the norm of the exact solution of the system is derived approximate responses of two particular linear slowly varying systems under external excitation are obtained by the proposed technique good agreement between the approximate and numerically obtained solutions is observed

output only cyclo stationary linear parameter time varying stochastic subspace identification method for rotating machinery and spinning structures abstract economical maintenance and operation are critical issues for rotating machinery and spinning structures containing blade elements especially large slender dynamic beams e g wind turbines structural health monitoring systems represent promising instruments to assure reliability and good performance from the dynamics of the mechanical systems however such devices have not been completely perfected for spinning structures these sensing technologies are typically informed by both mechanistic models coupled with data driven identification techniques in the time and or frequency domain frequency response functions are popular but are difficult to realize autonomously for structures of higher order especially when overlapping frequency content is present instead time domain techniques have shown to possess powerful advantages from a practical point of view i e low order computational effort suitable for real time or embedded algorithms and also are more suitable to differentiate closely related modes customarily time varying effects are often neglected or dismissed to simplify this analysis but such cannot be the case for sinusoidally loaded structures containing spinning multi bodies a more complex scenario is constituted when dealing with both periodic mechanisms responsible for the vibration shaft of the rotor blade system and the interaction of the supporting substructure transformations of the cyclic effects on the vibrational data can be applied to isolate inertial quantities that are different from rotation generated forces that are typically non stationary in nature after applying these transformations structural identification can be carried out by stationary techniques via data correlated eigensystem realizations in this paper an exploration of a periodic stationary or cyclo stationary subspace identification technique is presented here for spinning multi blade systems by means of a modified eigensystem realization algorithm era via stochastic subspace identification ssi and linear parameter time varying lptv techniques structural response is assumed to be stationary ambient excitation produced by a gaussian white noise within the operative range bandwidth of the machinery or structure in study era okid analysis is driven by correlation function matrices from the stationary ambient response aiming to reduce noise effects singular value decomposition svd and eigenvalue analysis are computed in a last stage to identify frequencies and complex valued mode shapes proposed assumptions are carefully weighted to account for the uncertainty of the environment a numerical example is carried out based a spinning finite element sfe model and verified using ansys ver 12 finally comments and observations are provided on how this subspace realization technique can be extended to the problem of modal parameter identification using only ambient vibration data

methods for stability evaluation for linear time varying discrete time systems on finite time horizon this paper develops a method for determining stability of discrete time dt linear time varying ltv systems defined on a finite time horizon fth in our considerations we use a collection of stability definitions for linear time invariant lti and ltv systems which are defined on an infinite time horizon ith based on the analysis carried out and the introduced operator matrix notation we define four stability functions these functions allow examination of the stability of a system described by an ltv state space model moreover using these functions we introduce the time stability margin and making use of the operator matrix notation we propose a method of determining the stability on a finite time horizon the theoretical considerations are numerically verified on two examples of ltv systems with a variable degree of non stationarity depending on a parameter e several examples illustrate the application of the introduced concepts and definitions to examination of the system stability also de

connes s trace theorem for curved noncommutative tori application to scalar curvature in this paper we prove a version of connes s trace theorem for noncommutative tori of any dimension n 2 this allows us to recover and improve earlier versions of this result in dimensions n 2 and n 4 by fathizadeh and khalkhali we also recover connes s integration formula for flat noncommutative tori of mcdonald sukochev and zanin as a further application we prove a curved version of this integration formula in terms of the laplace beltrami operator defined by an arbitrary riemannian metric for the class of the so called self compatible riemannian metrics including the conformally flat metrics of connes and tretkoff this shows that connes s noncommutative integral allows us to recover the riemannian density this exhibits a neat link between this notion of noncommutative integral and noncommutative measure theory in the sense of operator algebras as an application of these results we set up a natural notion of scalar curvature for curved noncommutative tori

identification of linear time varying systems abstract this paper is concerned with the identification of linear time varying systems the discrete time state space model of freely vibrating systems is used as an identification model the focus is placed on identifying successive discrete transition matrices that have the same eigenvalues as the original transition matrices first a typical subspace based method is presented to illustrate the extraction of the observability range space using the singular value decomposition svd of a general hankel matrix then the identification of varying transition matrices is approached by using an ensemble of response sequences for arbitrarily varying systems a series of the hankel matrices are formed by an ensemble set of responses which are obtained through multiple experiments on the system with the same time varying behaviour the varying transition matrix at each moment is estimated through the svd of two successive hankel matrices the proposed algorithm is applied to two special cases that require only a single response series i e periodically varying systems and slowly varying systems the use of the eigenvalues of the transition matrices is discussed and the pseudomodal parameters are defined finally a two link manipulator subjected to a varying end force is used as an example to illustrate the tracking capability and performance of the proposed algorithm

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

a class of subspace model identification algorithms to identify periodically and arbitrarily time varying systems abstract subspace model identification algorithms that allow the identification of a linear time varying ltv state space model from an ensemble set of input output measurements are presented in this paper each pair of input and output sequences in this ensemble is recorded when the underlying system to be identified undergoes the same time varying behavior the algorithms operate directly on the available ensemble of input output data and are a generalization of the recently proposed multivariable output error state space moesp class of algorithms to this ensemble type of identification problems a special case is considered in this paper where the repetition of this time varying behavior is intrinsic namely in periodically time varying systems an example of identifying a multirate sampled data system from a recorded input and output sequence demonstrates some of the capabilities of the presented subspace model identification algorithms

modal parameter estimation using the state space method abstract in modal parameter identification the damped complex exponential response methods extract modal parameters using free decay responses although there are several different complex exponential methods they are based on the prony method the prony method has some limitations such as poor robustness to noise computational burden and the unstable nature of root solver routines recent developments in signal processing indicate that model based eigendecomposition methods are very viable alternatives in this paper one of the model based eigendecomposition methods the state space method is first introduced the state space method makes use of the singular value decomposition svd to form a well conditioned data matrix and obtains the modal parameters through the eigendecomposition of the data matrix the paper then focuses on an analytical derivation of the svd of the data matrix in order to present a theoretical base for the method a simulation is used to illustrate important properties of the svd and performance of the state space method finally more applications of the svd of the data matrix are explored and the proposed applications are demonstrated by modal testing example it is shown that the state space method provides an elegant and robust tool for extracting modal parameters the svd of the data matrix offers significant information about the system order and mode participation of a free response

commutator structure of operator ideals commutator structure of operator ideals ken dykema 1 tadeusz figiel gary weiss and mariusz wodzicki department of mathematics texas a m university college station tx 77843 3368 usa b instytut matematyczny polskiej akademii nauk 81 825 sopot poland department of mathematical sciences university of cincinnati cincinnati oh 45221 0025 usa department of mathematics university of california berkeley ca 94720 3840 usa

interaction between a rigid inclusion and a line crack under uniform heat flux abstract the thermoelastic displacement boundary value problem for a rigid inclusion interacting with a line crack in an infinite plane subjected to a uniform heat flux is studied in which the rigid body rotation of the inclusion is considered to solve the prescribed problem we use the principle of superposition to decompose it into two groups of problems which are further reduced to several basic subproblems including green s functions of edge dislocation and heat source couple as well as the problem of a plane containing the inclusion under uniform heat flux and the problem of the inclusion subjected to a small rotation the problems are solved using the complex variable method along with the rational mapping function technique the variations of the stress intensity factors at the crack tips and the rigid body rotation angles with various crack lengths and heat flux angles are shown the effects of the inclusion shape and size are also investigated

generalized limits with additional invariance properties and their applications to noncommutative geometry abstract let n be the set of all natural numbers and l l n resp l l 0 be the banach space of all bounded sequences x x 1 x 2 resp classes of lebesgue measurable bounded functions on 0 with the uniform norm we work with subsets of the set of all normalized positive functionals on l and l which are used in noncommutative geometry to define various classes of dixmier traces singular positive traces on the ideal m 1 of compact operators on an infinite dimensional hilbert space h with logarithmic divergence of the partial sums of their singular values these classes of traces are of importance in noncommutative geometry and with each such a class say b of traces a subset m 1 b m 1 on which all traces from b coincide is linked the main objective of the present article is to give new characterizations of m 1 b for commonly occurring classes of dixmier traces we also answer a question from benameur and fack 2006 4 concerning conditions on a dixmier trace under which lidskii type formulae from that article hold

on multiple circular inclusions in plane thermoelasticity a general series solution to the problem of interacting circular inclusions in plane thermoelasticity is provided in this paper based upon the complex variable theory and the use of laurent series expansion the general expression of the stress functions is derived explicitly for the circular inclusion problem under remote uniform heat flow by applying the use of the superposition the problem dealing with any number of arbitrarily located inclusions can be then reduced to a set of linear algebraic equations which are solved with the aid of a perturbation technique for illustrating the use of the present approach an approximate closed form solution of the stress functions is derived explicitly for the problem containing two arbitrarily located inclusions numerical results of the interfacial stresses around a rigid circular inclusion or hoop stress along a circular hole due to the presence of an elastic inclusion are provided to demonstrate the dependence of the solution upon the pertinent parameters

quantum differentiability of essentially bounded functions on euclidean space abstract we investigate the properties of the singular values of the quantised derivatives of essentially bounded functions on r d with d 1 the commutator i sgn d 1 m f of an essentially bounded function f on r d acting by pointwise multiplication on l 2 r d and the sign of the dirac operator d acting on c 2 d 2 l 2 r d is called the quantised derivative of f we prove the condition that the function x f x 2 d 1 f x 2 d f x 2 d 2 x r d being integrable is necessary and sufficient for the quantised derivative of f to belong to the weak schatten d class this problem has been previously studied by rochberg and semmes and is also explored in a paper of connes sullivan and telemann here we give new and complete proofs using the methods of double operator integrals furthermore we prove a formula for the dixmier trace of the d th power of the absolute value of the quantised derivative for real valued f when x f x 2 d is integrable there exists a constant c d 0 such that for every continuous normalised trace on the weak trace class l 1 we have sgn d 1 m f d c d r d f x 2 d d x

subspace based identification of linear time varying system a physical parameter identification method for the linear time varying system is presented in this paper for an arbitrarily time varying system a series of hankel matrices are established directly from the combined measurements of displacement velocity and acceleration together with the input excitations from a single experiment with the system the time varying equivalent state space system matrices of the structure at each time instance are then identified by singular value decomposition using the free or random responses a time varying transformation matrix for transforming the identified equivalent system matrices into the physical system matrices is developed to determine the mass stiffness and damping matrices details of the proposed approach are investigated with a two degrees of freedom spring mass damper system with three kinds of time varying parameters numerical results show that the proposed method is accurate and effective in identifying time varying physical parameters

nonparametric time variant frequency response function estimates using arbitrary excitations the time variant frequency response function tv frf uniquely characterises the dynamic behaviour of a linear time variant ltv system this paper proposes a method for estimating nonparametrically the dynamic part of the tv frf from known input noisy output observations the arbitrary time variation of the tv frf is modelled by legendre polynomials in opposition to existing solutions the proposed method is applicable to arbitrary inputs

connes integration formula for the noncommutative plane our aim is to prove the integration formula on the noncommutative moyal plane in terms of singular traces a la connes

banach limits and traces on l1 abstract we introduce a new approach to traces on the principal ideal l 1 generated by any positive compact operator whose singular value sequence is the harmonic sequence distinct from the well known construction of j dixmier the new approach provides the explicit construction of every trace of every operator in l 1 in terms of translation invariant functionals applied to a sequence of restricted sums of eigenvalues the approach is based on a remarkable bijection between the set of all traces on l 1 and the set of all translation invariant functionals on l this bijection allows us to identify all known and commonly used subsets of traces dixmier traces connes dixmier traces etc in terms of invariance properties of linear functionals on l and definitively classify the measurability of operators in l 1 in terms of qualified convergence of sums of eigenvalues this classification has led us to a resolution of several open problems for the class l 1 from 7 as an application we extend connes classical trace theorem to positive normalised traces

dixmier traces are weak dense in the set of all fully symmetric traces abstract we extend dixmier s construction of singular traces see 2 to arbitrary fully symmetric operator ideals in fact we show that the set of dixmier traces is weak dense in the set of all fully symmetric traces that is those traces which respect hardy littlewood submajorization our results complement and extend earlier work of wodzicki 22

waterfilling theorems for linear time varying channels and related nonstationary sources the capacity of the linear time varying ltv channel a continuous time ltv filter with additive white gaussian noise is characterized by waterfilling in the time frequency plane similarly the rate distortion function for a related nonstationary source is characterized by reverse waterfilling in the time frequency plane constraints on the average energy or on the squared error distortion respectively are used the source is formed by the white gaussian noise response of the same ltv filter as before the proofs of both waterfilling theorems rely on a szeg theorem for a class of operators associated with the filter a self contained proof of the szeg theorem is given the waterfilling theorems compare well with the classical results of gallager and berger in the case of a nonstationary source it is observed that the part of the classical power spectral density is taken by the wigner ville spectrum the present approach is based on the spread weyl symbol of the ltv filter and is asymptotic in nature for the spreading factor a lower bound is suggested by means of an uncertainty inequality

the hochschild class of the chern character for semifinite spectral triples abstract we provide a proof of connes formula for a representative of the hochschild class of the chern character for p summable spectral triples our proof is valid for all semifinite von neumann algebras and all integral p 1 we employ the minimum possible hypotheses on the spectral triples

generalized evolutionary spectral analysis and the weyl spectrum of nonstationary random processes the evolutionary spectrum es is a time varying power spectrum of nonstationary random processes starting from an innovations system interpretation of the es we introduce the generalized evolutionary spectrum ges as a novel family of time varying power spectra the ges contains the es and the transitory evolutionary spectrum as special cases we consider the problem of finding an innovations system for a process characterized by its correlation function and we discuss the connection between ges analysis and the class of underspread processes furthermore we show that another special case of the ges a novel time varying power spectrum that we call the weyl spectrum has substantial advantages over all other members of the ges family the properties of the weyl spectrum are discussed and its superior performance is verified experimentally for synthetic and real data processes

moving kriging shape function modeling of vector tarma models for modal identification of linear time varying structural systems abstract this work proposes a moving kriging mk shape function modeling method for modal identification of linear time varying ltv structural systems based on vector time dependent autoregressive moving average vtarma models it aims to avoid the functional subspaces selection of the conventional functional series vtarma fs vtarma models instead of the common basis functions it constructs the time varying coefficients on the time nodes with the mk shape functions in a compact support domain the merit of the mk shape function is to determine its shape parameters upon vector random vibration signals adaptively model identification is effectively dealt with through an optimization scheme that decomposes the identification problem into two subproblems estimating model parameters via two stage least squares 2sls method and estimating shape function parameters via a discrete continuous variable hybrid optimization in addition the model order selection is achieved by the optimization scheme this method has been validated by a monte carlo study of simulation case and further by an experimental test case and the performance and potential advantages are illustrated

an input output based procedure for fully evaluating and monitoring dynamic properties of structural systems via a subspace identification method abstract dynamic behaviour of complex structural systems may be modelled by a system of second order linear ordinary differential equations i e m t d t sw t f t by means of either structural analysis for finite degree of freedom systems or discretization procedures e g fe methods for continuous systems here w t and f t are the displacement vector and the force vector owing to erosion friction and internal damage and cracks etc a working process of a system always accompanies gradual degradation of the performance of this system the stiffness of the system weakens whereas the damping of the system strengthens to evaluate such degradation the usual way is to model the evolution of property of a system obtain system property parameters trace the history of motion and loading carry out complicated analysis and computation under prescribed initial and boundary value conditions and finally derive the degraded property and responses of the system this traditional way however might be cumbersome and unsatisfactory in some cases due to the lack of adequate experimental data and well founded theoretical basis etc another way is to apply inverse methods such as modal analysis methods with fft and a subspace identification method etc developed in the theory of system identification which extracts information about system properties directly from experimental input output measurement data and hence do not involve the foregoing traditional analysis the latter method however could not supply full information about system properties due to the assumption of the black box viewpoint in this work with suitable experimental input output measurement data a simple effective procedure is described by which the stiffness matrix s and the damping matrix d may be determined in a complete unique manner using a subspace identification method the possibility of such a procedure arises from the observation of the self evident fact the conservation of mass of any part of a structural system implies that the mass matrix m of this system is constant and hence is given by its initial value the stiffness and damping matrices s and d determined by the proposed procedure may be used to evaluate and monitor in a full sense the degradation of dynamic properties of structural systems further with the information about the stiffness distribution of constituent elements of a structural system it is shown that it may be possible to estimate the locations of the damaged or faulty elements in this system an example is given to illustrate the application of the proposed procedure