resolution bias errors in spectral density frequency response and coherence function measurements vi non white noise at the input the general theory of spectral estimation presented in a previous part of this series of papers is applied exemplarily to the case of a non white 1 f 2 noise excited rc low pass filter it is shown that the differences compared to the case of white noise excitation observed in the frequency response and coherence estimates are small if the hanning or another continuous window is used but that they can become drastic for the rectangular window experimental results are in accord with the theoretical prediction further experiments with an electrical lrc resonance circuit second order system show that the same applies in this case

resolution bias errors in spectral density frequency response and coherence function measurements iii application to second order systems white noise excitation a general theory of spectral estimation given in a previous paper is applied to second order systems such as a simple spring mass system where either the displacement velocity or acceleration of the vibrating mass may be considered as the output signals by means of approximate formulas an extensive bias error discussion of frequency response output power spectral density and coherence estimates is given which clarifies characteristic differences between spectral estimators obtained with the rectangular window on the one hand and the hanning window or another continuous window on the other hand in particular characteristic coherence notches in the measurement of resonance systems as reported in the literature are explained from first principles all of the theoretical predictions are verified experimentally to great accuracy by using electrical lrc resonance circuits which are equivalent to the respective mechanical systems

resolution bias errors in spectral density frequency response and coherence function measurements i general theory a general theory of resolution bias errors inherent in the usual ensemble segment averaging estimation procedure for spectral density frequency response and coherence functions has been developed it is shown that the estimation procedure is mathematically equivalent to a situation where the true correlation functions would be modified in a specified manner that is they would be multiplied with the normalized autocorrelation function of the window function and transformed into the frequency domain to yield the spectral density estimates the theory is worked out for an arbitrary ideal linear and time invariant system which is driven by a stationary stochastic input and for an arbitrary window function specifically the rectangular and hanning windows are compared with each other and the theoretical results are verified experimentally to great accuracy by using electrical rc and lrc circuits and a true random noise generator see later parts of this series of papers furthermore as an application of the theory approximate formulas for the bias errors of spectral estimators are derived and discussed thus extending some older results given in the literature

estimation of fmri response delays we present an efficient algorithm using the hilbert transform for estimating the delay of the bold response to neuronal stimulation with minimal additional computations the algorithm estimates parameters generated in the widely used cross correlation method and simplifies the interpolation required to estimate the response delay from the cross correlation function we examined errors in the hilbert based delay estimate associated with the use of dft on short duration discrete signals and proposed a method for minimizing these errors furthermore we compared the delay estimates obtained with the hilbert method to those obtained using the onset of the bold response the hilbert method resulted in less variance in the delay estimate despite the potential for higher variability in the latter part of the bold response this improved delay estimate was attributed to the reduced sensitivity of the hilbert method to noise contamination compared to the onset method

minimal realization of nonlinear systems described by input output difference equations we consider a general class of nonlinear discrete time systems described by their input output i o relationship we first present the necessary and sufficient conditions for existence of a local observable state space realization of the system and an explicit algorithm for computing it in cases where the i o map and its resulting realization are nonminimal we formulate an algorithm for extracting its minimal realization whenever possible the developed theory and algorithms are illustrated by means of several examples

finite volterra series realizations and input output approximations of non linear discrete time systems abstract it is shown that a separability property of a given finite family of stationary kernels turns out to be necessary and sufficient for the realization of the associated functional by means of a polynomial affine system i e a system that is polynomial in the input and affine in the state moreover the discrete volterra kernels associated with the input output map of a non linear analytic discrete lime system initialized at an equilibrium point are shown to possess a separability property on this basis we state an approximation result for the given input output map by considering the first kernels of the discrete volterra series two explicit constructions of the approximating polynomial affine systems are proposed

brief transfer equivalence and realization of nonlinear higher order input output difference equations two fundamental modelling problems in nonlinear discrete time control systems are studied using the language of differential forms the discrete time nonlinear single input single output systems to be studied are described by input output i o difference equations i e a high order difference equation relating the input the output and a finite number of their time shifts a new definition of equivalence is introduced which generalizes the notion of transfer equivalence well known for the linear case our definition is based upon the notion of an irreducible differential form of the system and was inspired by the analogous definition for continuous time systems the second problem to be addressed is the realization problem the i o difference equation is assumed to be in the irreducible form so that one can obtain an accessible and observable realization necessary and sufficient conditions are given for the existence of a local state space realization of the irreducible i o difference equation these conditions are formulated in terms of the integrability of certain subspaces of one forms classified according to their relative degree the sufficiency part of the proof gives a constructive procedure up to finding the integrating factors and integration of the set of one forms for obtaining a locally observable and accessible state space system if the system is not in the irreducible form one has first to apply the reduction procedure to transform the system into the irreducible form

application of multivariate uncertainty analysis to frequency response function estimates uncertainty estimation is an important part of any measurement but is often neglected for complex valued or multivariate data e g vectors this paper presents a methodology for estimating the uncertainty in multivariate experimental data and applies it to the measurement of the frequency response function obtained when using a periodic random input signal this multivariate uncertainty method is an extension of classical uncertainty methods used for scalar variables and tracks the correlation between all variates along with the sample variance instead of just tracking the standard uncertainty the method is used in this paper to propagate the sample covariance matrix from spectral density estimates to the uncertainty in the frequency response function estimate for two different system models in the first model the case when only the output signal is corrupted by noise is considered while in the second model both the input and output signals are corrupted by uncorrelated noise sources the results for the single noise model are verified by comparing them to published expressions in the literature while the results for the two noise model are verified by using a direct computation of the statistics finally the method is applied to experimental data from two microphone measurements within an acoustic waveguide the random uncertainty estimates in the frequency response function from the multivariate method agree well with the results from a direct computation of the statistics

artin rings of global dimension two in this paper we show that a left artin ring a of global dimension at most two has loewy length at most 2 1 where n is the number of simple components of a rad a we assume that the reader is familiar with the trends but not necessarily the details of contemporary representation theory of artin rings let us record a few conventions the rings discussed here will be left artinian unless otherwise specified and will sometimes be finite dimensional algebras over an algebraically closed field henceforth denoted by k modules will be finitely generated left modules unless otherwise specified the radical of a will usually be denoted by r the loewy

tame algebras and tits quadratic forms abstract we solve a long standing problem concerning the connection between the tameness of simply connected algebras and the weak nonnegativity of the associated tits integral quadratic forms and derive some consequences

the effect of bandwidth on the accuracy of transfer function measurements of single degree of freedom system response to random excitation abstract whenever random excitation is used in the determination of frequency response functions for a single degree of freedom system the measurement accuracy depends on the frequency resolution of the measurement technique if the ratio of measurement bandwidth to the 3 db bandwidth of the resonance is too great negative bias errors occur at resonance in estimates of power spectral levels and the transfer function parameters of amplitude and coherence numerical integration has been used to calculate teh expected errors that result whenever hanning or kaiser bessel weighting is applied in a fast fourier transform fft analysis and the errors that would be expected if an idealized rectangular frequency domain filter could be employed have also been similarly derived the numerical data are presented and compared with appropriate experimental data

strongly simply connected schurian algebras and multiplicative bases abstract in this paper we define concepts of crowns and quasi crowns valid in an arbitrary schurian algebra and which generalise the corresponding concepts in an incidence algebra we show first that a triangular schurian algebra is strongly simply connected if and only if it is simply connected and contains no quasi crown we then prove that the absence of quasi crowns in a triangular schurian algebra implies the existence of a multiplicative basis

the immersion under feedback of a multidimensional discrete time non linear system into a linear system this paper deals with the problem of finding conditions which ensure the reproducibility of the input output behaviour of a linear analytic discrete time system by means of a linear discrete time system on this basis the problem of modifying the system by feedback in order for it to enjoy such a property is posed and solved

resolution bias errors in spectral density frequency response and coherence function measurements iv time delay bias errors the problem of time delay bias errors is treated in this part of the present series of papers as a special case of a general theory of resolution bias errors in spectral estimation presented in a previous part it is shown that the main effect of an additional time delay between the output and the input of a physical system is to multiply the frequency response and coherence estimators which would be obtained without delay with the normalized autocorrelation function of the window function and its square respectively experimental results for the rectangular and hanning windows are in accord with the theoretical predictions the theoretical results given in the literature previously are valid for the rectangular window only but not for an arbitrary window function

lie stacks and their enveloping algebras abstract a lie stack is an algebra morphisms a a bwhereaandbare finite dimensional c algebras withbbeing augmented local we construct the enveloping algebrau s of a lie stack and show that it is an irreducible hopf algebra domain with a poincare birkhoff witt basis we recover the enveloping algebrasu g of lie algebras as special instances we give conditions such thatu s is neither commutative nor cocommutative and we give such examples forbbeing any non commutative augmented local algebra and for beingathe path algebra of a suitable bipartite quiver by studying orbit closes in the variety of lie stacks of fixed dimension one obtains in this way deformations of enveloping algebras of lie algebras

from chronological calculus to exponential representations of continuous and discrete time dynamics a lie algebraic approach in this paper formal exponential representations of the solutions to nonautonomous nonlinear differential equations are derived it is shown that the chronological exponential admits an ordinary exponential representation the exponent being given by an explicitly computable lie series expansion the results are then used to describe controlled dynamics dynamics under sampling and forced discrete time dynamics the study emphasizes the role of lie algebra techniques in nonlinear control theory and specifies structural similarities between nonautonomous differential equations dynamics under sampling and forced discrete time dynamics up to hybrid ones

multiplicative bases in matrix algebras abstract in a finite dimensional algebra over a field f a basis b is called a multiplicative basis provided that b 0 forms a semigroup we will describe all multiplicative bases of fn the full algebra of n n matrices over a subfield f of the real numbers every such basis is associated with a nonsingular zero one matrix via a lattice order on fn this association is a one to one correspondence after identification of isomorphic semigroups and identification of the zero one matrices that have just permuted rows and columns this correspondence yields an enumeration method for nonequivalent multiplicative bases of fn the enumeration is done for n 5

the strong no loop conjecture for mild algebras abstract let be a finite dimensional associative algebra over an algebraically closed field with a simple module s of finite projective dimension the strong no loop conjecture says that this implies ext 1 s s 0 i e that the quiver of has no loop at the point corresponding to s in this paper we prove the conjecture in case is mild which means that has a distributive lattice of two sided ideals and each proper factor algebra j is representation finite in fact it is sufficient that a small neighborhood of the support of the projective cover of s is mild

resolution bias errors in spectral density frequency response and coherence function measurements v comparison of different frequency response estimators three different types of frequency response estimators are considered and compared with each other with respect to the inherent resolution bias errors the behavior of these estimators is shown to differ considerably especially with respect to peak estimation in resonance systems such as a simple spring mass system one of these estimators is shown to exhibit almost no peak bias error at resonance under noise free measurement conditions whereas the peak bias error of the estimator most commonly used is maximum however aside from resonance the peak bias free estimator proves to be the worst of the three estimators the theoretical predictions are accurately verified by experiments with an electrical lrc resonance circuit

the algebras with discrete derived category abstract we classify the finite dimensional algebras over an algebraically closed field whose bounded derived category does not admit an infinite continuous family of pairwise non isomorphic indecomposable complexes

automorphisms of representation finite algebras coverings in representation theory have been successfully used by bongartzgabriel 2 gabriel 3 green 4 riedtman 6 7 of particular importance is the study of the relations between the coverings of the auslander reiten quiver and the ordinary quiver in this direction p gabriel posed in the third international conference on representations of algebras puebla m6xico 1980 the following conjecture let g be an automorphism of an algebra a of finite representation type for each right module m denote by m g the a module with underlying group m and scalar multiplication m 2 mgl 2 if sgq s for each simple s then m g q m for each indecomposable m the aim of this note is to give a short proof of this statement the conjecture is not true for algebras of infinite representation type con

weakly ordered multiplicative basis of an algebra related to quiver theory abstract in this paper for an algebra a multiplicative basis with a weakly admissible order is introduced as an invariant under almost morita equivalence it is shown that an algebra with a weakly ordered multiplicative basis is a quotient of its corresponding generalized path algebra which is a generalization of the classical gabriel structure theorem finally it is proven that the skew group algebra of a cyclic group over an algebra with an ordered multiplicative basis has a weakly ordered multiplicative basis

covering functors without groups coverings in the representation theory of algebras were introduced for the auslander reiten quiver of a representation finite algebra in ch riedtmann algebren darstellungskocher uberlagerungen und zuruch comment math helv 55 1980 199 224 and later for finite dimensional algebras in k bongartz p gabriel covering spaces in representation theory invent math 65 3 1982 331 378 p gabriel the universal cover of a representation finite algebra in proc representation theory i puebla 1980 in lecture notes in math vol 903 springer 1981 pp 68 105 r martinez villa j a de la pena the universal cover of a quiver with relations j pure appl algebra 30 3 1983 277 292 the best understood class of covering functors is that of galois covering functors f a b determined by the action of a group of automorphisms of a in this work we introduce the balanced covering functors which include the galois class and for which classical galois covering type results still hold for instance if f a b is a balanced covering functor where a and b are linear categories over an algebraically closed field and b is tame then a is tame

delayed block transfer function in the frequency domain when the impulse response of a transfer system is long it is difficult for the standard cross spectrum method to obtain an accurate estimate of the transfer function by applying the fast fourier transform fft with a finite length window the bias error in the estimate is large especially around the resonant frequency of the transfer system in the paper therefore the authors propose an alternative new method to obtain an accurate estimate of the transfer function the delayed block transfer function is introduced to detect the components that are correlated to the signal in the input window but leak from the output window based on these transfer functions the total characteristics of the transfer system are estimated accurately in the latter half of the paper the authors derive the theoretical expressions for the bias errors in the transfer functions estimated by the proposed and the standard methods by thoroughly comparing the resultant expressions the superiority and the usefulness of the proposed method are theoretically confirmed finally the simulation experiments show the advantages of the proposed method

bias in the cross spectrum and time delay estimates due to misalignment the effect of misalignment in the weighted overlapped segment averaging method used for estimating time delay is investigated with nonwhite input it is shown that the phase of the cross spectrum and the location of the peak in the cross correlator are biased

algebras with cycle finite galois coverings we prove that the finite dimensional algebras over an algebraically closed field which admit cycle finite galois coverings with torsion free galois groups are of tame representation type and derive some consequences

cartan leray spectral sequence for galois coverings of linear categories abstract we provide a cartan leray type spectral sequence for the hochschild mitchell co homology of a galois covering of linear categories we infer results relating the galois group and hochschild cohomology in degree one

a characterization of finite ei categories with hereditary category algebras abstract in this paper we give an explicit algorithm to construct the ordinary quiver of a finite ei category for which the endomorphism groups of all objects have orders invertible in the field k we classify all finite ei categories with hereditary category algebras characterizing them as free ei categories in a sense which we define for which all endomorphism groups of objects have invertible orders some applications on the representation types of finite ei categories are derived

uncertainty analysis of the two microphone method accurate duct acoustic propagation models are required to characterize and subsequently reduce aircraft engine noise the boundary conditions for these models ultimately rely on accurate measurements of the acoustic impedance for candidate nacelle liners the standard two microphone method is widely used to estimate acoustic impedance but does not provide uncertainty estimates that are essential for data quality assessment and model validation a systematic framework is presented in this paper to propagate the experimental 95 confidence interval uncertainty estimates in the measured quantities to the calculated acoustic impedance data using the two microphone method for small and large input uncertainties one method is an analytical small perturbation technique using multivariate statistics this method provides useful analytical scaling information a second monte carlo method is utilized to validate the analytical multivariate method both methods are applied to the two microphone method for simulated data representative of sound hard and sound soft acoustic materials the results indicate that for realistic experimental parameters the uncertainty in the input measurements results in nonlinear perturbations therefore the small perturbation technique fails and the monte carlo method should be used to obtain uncertainty estimates furthermore the nonlinear perturbations also distort the output statistical distributions of the calculated acoustic impedance and reflection coefficient which results in significant deviation from gaussian behavior the distortion is a function of the acoustic impedance of the specimen itself finally the monte carlo method is applied to experimental data for a ceramic tubular specimen and compared to the multivariate results to demonstrate the implementation and usefulness of the technique