an adams riemann roch theorem in arakelov geometry we prove an analog of the classical riemann roch theorem for adams operations acting on k theory in the context of arakelov geometry

analytic torsion and holomorphic determinant bundles in this paper we prove that in the case of holomorphic locally kahler fibrations the analytic and algebraic geometry constructions of determinant bundles for direct images coincide we calculate the curvature of the holomorphic hermitian connection for the quillen metric on the determinant bundle we study the behavior of the quillen metric under change of metrics in the fibers and also on the twisting vector bundles we thus generalize the conformal anomaly formula to kahler manifolds of arbitrary dimension we also study the quillen metrics on determinants associated with exact sequences of vector bundles we prove that the quillen metric is smooth on the grothendieck knudsen mumford determinant for arbitrary holomorphic fibrations

analytic torsion and holomorphic determinant bundles i bott chern forms and analytic torsion we attach secondary invariants to any acyclic complex of holomorphic hermitian vector bundles on a complex manifold these were first introduced by bott and chern bot c our new definition uses quillen s superconnections we also give an axiomatic characterization of these classes these results will be used in bgs2 and bgs3 to study the determinant of the cohomology of a holomorphic vector bundle

dynamical systems associated to separated graphs graph algebras and paradoxical decompositions abstract we attach to each finite bipartite separated graph e c a partial dynamical system e c f where e c is a zero dimensional metrizable compact space f is a finitely generated free group and is a continuous partial action of f on e c the full crossed product c algebra o e c c e c f is shown to be a canonical quotient of the graph c algebra c e c of the separated graph e c similarly we prove that for any field k the algebraic crossed product l k ab e c c k e c alg f is a canonical quotient of the leavitt path algebra l k e c of e c the monoid v l k ab e c of isomorphism classes of finitely generated projective modules over l k ab e c is explicitly computed in terms of monoids associated to a canonical sequence of separated graphs using this we are able to construct an action of a finitely generated free group f on a zero dimensional metrizable compact space z such that the type semigroup s z f k is not almost unperforated where k denotes the algebra of clopen subsets of z finally we obtain a characterization of the separated graphs e c such that the canonical partial action of f on e c is topologically free

orbifolds and analytic torsions dans cet article on calcule le comportement de metrique de quillen par immersions d orbifold on etend ainsi une formule de bismut lebeau au cas d orbifold

output frequencies of nonlinear systems an explicit expression for the output frequency range of nonlinear systems for general inputs is derived this reveals the relationship between the input and output frequency ranges of a nonlinear system and extends the well known concept in linear systems where the output frequency range is exactly the same as that of the corresponding input the new results provide an important and basic relationship that can be applied in nonlinear system frequency domain analysis and design

a fixed point formula of lefschetz type in arakelov geometry i statement and proof we consider arithmetic varieties endowed with an action of the group scheme of n th roots of unity and we define equivariant arithmetic k 0 theory for these varieties we use the equivariant analytic torsion to define direct image maps in this context and we prove a riemann roch theorem for the natural transformation of equivariant arithmetic k 0 theory induced by the restriction to the fixed point scheme this theorem can be viewed as an analog in the context of arakelov geometry of the regular case of the theorem proved by p baum w fulton and g quart in bafq we show that it implies an equivariant refinement of the arithmetic riemann roch theorem in a form conjectured by j m bismut cf b2 par l p 353 and also ch soule s question in sabk 1 5 p 162

amenability and paradoxicality in semigroups and c algebras abstract we analyze the dichotomy amenable paradoxical in the context of discrete countable unital semigroups and corresponding semigroup rings we consider also folner type characterizations of amenability and give an example of a semigroup whose semigroup ring is algebraically amenable but has no folner sequence in the context of inverse semigroups s we give a characterization of invariant measures on s in the sense of day in terms of two notions domain measurability and localization given a unital representation of s in terms of partial bijections on some set x we define a natural generalization of the uniform roe algebra of a group which we denote by r x we show that the following notions are then equivalent 1 x is domain measurable 2 x is not paradoxical 3 x satisfies the domain folner condition 4 there is an algebraically amenable dense subalgebra of r x 5 r x has an amenable trace 6 r x is not properly infinite and 7 0 1 in the k 0 group of r x we also show that any tracial state on r x is amenable moreover taking into account the localization condition we give several c algebraic characterizations of the amenability of x finally we show that for a certain class of inverse semigroups the quasidiagonality of c r x implies the amenability of x the reverse implication which is a natural generalization of rosenberg s conjecture to this context is false

the design of energy transfer filters for energy focus filtering this paper is concerned with extending the energy transfer filters etfs designs to a more general case where the design requirement is to focus signal energy from different input frequency bands into a desired output frequency range etfs are a class of non linear filters recently proposed by the authors to employ non linear effects to transfer signal energy from one frequency band to a different frequency location the new etf designs considered in the present study involve the development of an algorithm for determining output frequencies of non linear systems subject to an input the frequency components of which are located in two separate frequency intervals and a new procedure for the implementation of the filter design the results achieved provide an effective approach to the solution to a more general etf design problem

stabilizing predictive control of nonlinear arx models in this paper a predictive control algorithm for nonlinear discrete time systems is presented starting from a state space model conditions for the asymptotic tracking of constant reference signals in a neighbourhood of a given equilibrium are first derived then it is shown that the system under control can be locally described in terms of a suitable narx nonlinear arx model which in practice can be identified by means of well established techniques for the narx model a receding horizon predictive control algorithm is proposed which guarantees local stability and robust asymptotic tracking in the neighbourhood of the equilibrium conditions for local stability and tracking are given in terms of reachability observability and transmission zeros of the linearization of the original state space system around the equilibrium an example is reported to illustrate the effectiveness of the proposed method

the atiyah singer theorems a probabilistic approach ii the lefschetz fixed point formulas abstract in this paper the lefschetz fixed point formulas of m f atiyah and i m singer ann of math 87 1968 484 530 546 604 for classical elliptic complexes are proved by using probabilistic methods

a new method for the design of energy transfer filters this paper is concerned with the development of a new method for the design of energy transfer filters etfs etfs are a new class of non linear filters recently proposed by the authors which employ non linear effects to transfer signal energy from one frequency band to a different frequency location the new method uses the powerful orthogonal least squares ols algorithm to solve the least squares problem associated with the design and compared with previous methods achieves much better filtering performance

use of press residuals in dynamic system identification cross validation whereby the data is split into an estimation set and a prediction set is often used for model structure selection in dynamic system identification a related approach that simulates cross validation without requiring two sets of data is to compute the weighted residuals of the least squares estimated model that represent the true prediction errors the sum of the squared true prediction errors is defined as the press this paper will show that the computation of the press is straightforward when using an orthogonal decomposition algorithm to obtain the least squares model parameter estimates a benchmark example of ljung is used to illustrate how the press is applied for model structure selection

k3 surfaces with involution equivariant analytic torsion and automorphic forms on the moduli space in this paper we introduce an invariant of a k3 surface with 2 action equipped with a 2 invariant kahler metric which we obtain using the equivariant analytic torsion of the trivial line bundle this invariant is shown to be independent of the choice of the kahler metric it can be viewed as a function on the moduli space of k3 surfaces with involution the main result of this paper is that this function can be identified with an automorphic form which characterizes the discriminant locus in particular we show that the ray singer analytic torsion of the trivial line bundle on an enriques surface with ricci flat kahler metric is given by the value of the norm of the borcherds function at its period point

recursive algorithm for computing the frequency response of a class of non linear difference equation models abstract a recursive algorithm is developed which is both computationally compact and enables the nth order frequency response functions of a large class of non linear difference equation models to be found without restriction on the order n

superconnection currents and complex immersions let i m m be an immersion of complex manifolds and let be a complex of holomorphic hermitian vector bundles on m which provides a projective resolution of the sheaf of sections of a holomorphic vector bundle on m we study the convergence as u of a class of superconnection currents u introduced by quillen and we calculate the limit microlocal estimates of the speed of convergence are also given

real embedding and equivariant eta forms bismut and zhang math ann 295 4 661 684 1993 establish a mathrm mod mathbb z embedding formula of atiyah patodi singer reduced eta invariants in this paper we explain the hidden mathrm mod mathbb z term as a spectral flow and extend this embedding formula to the equivariant family case in this case the spectral flow is generalized to the equivariant chern character of some equivariant dai zhang higher spectral flow

the amenability of affine algebras abstract we introduce the notion of amenability for affine algebras we characterize amenability by folner sequences paradoxicality and the existence of finitely invariant dimension measures then we extend the results of rowen on ranks from affine algebras of subexponential growth to amenable affine algebras

the atiyah singer index theorem for families of dirac operators two heat equation proofs the purpose of this paper is to give two heat equation proofs of the index theorem of atiyah singer for a family of dirac operators

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

finite input output representative of a class of volterra polynomial systems n this paper the problem of finite input output representation of a special class of nonlinear volterra polynomial systems is studied via the notion of linear factorization of d series this is an algebraic method based mainly on the star product operation and on a related euclidean type algorithm

nonlinear filters based on combinations of piecewise polynomials with compact support when nonlinear filters are designed based on input output observations the descriptive nonlinear transformation between the input and the output signals is often unknown filters with generalized models are therefore required for a good characterization of these cases in this paper we introduce a class of filters obtained from the additive combination of multiple kernels each kernel constitutes a localized model for the desired nonlinear mapping and is defined as a multivariate continuous piecewise polynomial cpp function with compact support by bringing together the efficiency of piecewise polynomial approximations and the flexibility of kernel combinations we end up with models able to represent effectively a broad variety of nonlinearities a localized threshold decomposition operator ltd is introduced to provide closed form expressions for continuous nonsmooth kernels whereas the method of splines is used to derive smooth functionals simple equalization problems involving nonlinear nonminimum phase and non gaussian channels are used to examine the advantages of the proposed methods and compare them with other conventional alternatives

identification of mimo non linear systems using a forward regression orthogonal estimator abstract an orthogonal least squares estimator which was originally derived for single input single output systems is extended to multi input multi output non linear systems the estimator can provide information about the structure or which terms to include in the model and final parameter estimates in a very simple and efficient manner multivariable non linear model validity tests are also discussed and the results of applying the orthogonal estimator to both simulated and real data are included

output frequency characteristics of nonlinear systems some interesting properties of output frequencies of volterra type nonlinear systems are particularly investigated these results provide a very novel and useful insight into the super harmonic and inter modulation phenomena in output frequency response of nonlinear systems with consideration of the effects incurred by different nonlinear components in the system the new properties theoretically demonstrate several fundamental output frequency characteristics and unveil clearly the mechanism of the interaction or coupling effects between different harmonic behaviors in system output frequency response incurred by different nonlinear components these results have significance in the analysis and design of nonlinear systems and nonlinear filters in order to achieve a specific output spectrum in a desired frequency band by taking advantage of nonlinearities they can provide an important guidance to modeling identification control and signal processing by using the volterra series theory in practice

a fixed point formula of lefschetz type in arakelov geometry iii representations of chevalley schemes and heights of flag varieties we give a new proof of the jantzen sum formula for integral representations of chevalley schemes over spec z except for three exceptional cases this is done by applying the fixed point formula of lefschetz type in arakelov geometry to generalized flag varieties our proof involves the computation of the equivariant ray singer torsion for all equivariant bundles over complex homogeneous spaces furthermore we find several explicit formulae for the global height of any generalized flag variety

representations of non linear systems the narmax model abstract input output representations of non linear discrete time systems are discussed it is shown that the narmax non linear autoregressive moving average with exogenous inputs model is a general and natural representation of non linear systems and contains as special cases several existing non linear models the problem of approximating non linear input output systems is also addressed and several properties of non linear models are highlighted using simple examples