weakly lefschetz symplectic manifolds for a symplectic manifold the harmonic cohomology of symplectic divisors introduced by donaldson 1996 and of the more general symplectic zero loci introduced by auroux 1997 are compared with that of its ambient space we also study symplectic manifolds satisfying a weakly lefschetz property that is the s lefschetz property in particular we consider the symplectic blow ups cp m of the complex projective space cp m along weakly lefschetz symplectic submanifolds m cp m as an application we construct for each even integer s 2 compact symplectic manifolds which are s lefschetz but not s 1 lefschetz

new approaches without postprocessing to fir system identification using selected order cumulants in this paper we address the problem of identifying the parameters of the nonminimum phase fir system from the cumulants of noisy output samples the system is driven by an unobservable zero mean independent and identically distributed i i d non gaussian signal the measurement noise may be white gaussian colored ma arma gaussian processes or even real for this problem two novel methods are proposed the methods are designed by using higher order cumulants with the following advantages i flexibility method 1 employs two arbitrary adjacent order cumulants of output whereas method 2 uses three cumulants of output two cumulants with arbitrary orders and the other one with an order equal to the summation of the two orders minus one because of this flexibility we can select cumulants with appropriate orders to accommodate different applications ii linearity both the formulations in method 1 and method 2 are linear with respect to the unknowns unlike the existing cumulant based algorithms the post processing is thus avoided extensive experiments with arma gaussian and three real noises show that the new algorithms especially algorithm 1 perform the fir system identification with higher efficiency and better accuracy as compared with the related algorithms in the literature

poisson harmonic forms kostant harmonic forms and the s1 equivariant cohomology ofk t abstract we characterize the harmonic forms on a flag manifold k t defined by kostant in 1963 in terms of a poisson structure namely they are poisson harmonic with respect to the so called bruhat poisson structure on k t this enables us to give poisson geometrical proofs of many of the special properties of these harmonic forms in particular we construct explicit representatives for the schubert basis of the s 1 equivariant cohomology of k t where the s 1 action is defined by using a simple argument in equivariant cohomology we recover the connection between the kostant harmonic forms and the schubert calculus on k t that was found by kostant and kumar in 1986 by using a family of symplectic structures on k t we also show that the kostant harmonic forms are limits of the more familiar hodge harmonic forms with respect to a family of hermitian metrics on k t

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

batalin vilkovisky quantization and the algebraic index abstract into a geometric setting we import the physical interpretation of index theorems via semi classical analysis in topological quantum field theory we develop a direct relationship between fedosov s deformation quantization of a symplectic manifold x and the batalin vilkovisky bv quantization of a one dimensional sigma model with target x this model is a quantum field theory of aksz type and is quantized rigorously using costello s homotopic theory of effective renormalization we show that fedosov s abelian connections on the weyl bundle produce solutions to the effective quantum master equation moreover bv integration produces a natural trace map on the deformation quantized algebra this formulation allows us to exploit a rigorous localization argument in quantum field theory to deduce the algebraic index theorem via semi classical analysis i e one loop feynman diagram computations

lichnerowicz jacobi cohomology in this paper we extend the notion of lichnerowicz poisson cohomology to jacobi manifolds we study the relation of the so called lichnerowicz jacobi cohomology with the basic de rham cohomology and the cohomology of the lie algebra of functions relative to the representation defined by the hamiltonian vector fields a natural pairing with the canonical homology is constructed the relation between the lichnerowicz poisson cohomology of a quantizable poisson manifold and the lichnerowicz jacobi cohomology of the total space of a prequantization bundle is obtained particular cases of cosymplectic contact and locally conformal symplectic manifolds are discussed finally the lichnerowicz jacobi cohomology of a non transitive example is studied

iterative construction of fixed points of asymptotically nonexpansive mappings abstract let t be a completely continuous and asymptotically nonexpansive self mapping of a nonempty closed bounded and convex subset of a hilbert space then under certain conditions the sequence defined by xn 1 ntn xn 1 n x n converges strongly to some fixed point of t a similar result is obtained for asymptotically pseudocontractive mappings whose iterates are lipschitz continuous with respect to some common lipschitz constant

homology of pseudodifferential operators on manifolds with fibered cusps the hochschild homology of the algebra of pseudodifferential operators on a manifold with fibered cusps introduced by mazzeo and melrose is studied and computed using the approach of brylinski and getzler one of the main technical tools is a new convergence criterion for tri filtered half plane spectral sequences using trace like functionals that generate the 0 dimensional hochschild cohomology groups the index of a fully elliptic fibered cusp operator is expressed as the sum of a local contribution of atiyah singer type and a global term on the boundary we announce a result relating this boundary term to the adiabatic limit of the eta invariant in a particular case

cumulant based identification approaches for nonminimum phase fir systems recursive and least squares methods for identification of non minimum phase linear time invariant nmp lti fir systems are developed the methods utilize the second and third order cumulants of the output of the fir system whose input is an independent identically distributed i i d non gaussian process since knowledge of the system order is of utmost importance to many system identification algorithms new procedures for determining the order of an fir system using only the output cumulants are also presented to illustrate the effectiveness of the methods various simulation examples are presented

poisson homology in degree 0 for some rings of symplectic invariants abstract let g be a finite dimensional semi simple lie algebra h a cartan subalgebra of g and w its weyl group the group w acts diagonally on v h h as well as on c v the purpose of this article is to study the poisson homology of the algebra of invariants c v w endowed with the standard symplectic bracket to begin with we give general results about the poisson homology space in degree 0 denoted by hp 0 c v w in the case where g is of type b n c n or d n results which support alev s conjecture then we are focusing the interest on the particular cases of ranks 2 and 3 by computing the poisson homology space in degree 0 in the cases where g is of type b 2 so 5 d 2 so 4 then b 3 so 7 and d 3 a 3 so 6 sl 4 in order to do this we make use of a functional equation introduced by y berest p etingof and v ginzburg we recover by a different method the result established by j alev and l foissy according to which the dimension of hp 0 c v w equals 2 for b 2 then we calculate the dimension of this space and we show that it is equal to 1 for d 2 we also calculate it for the rank 3 cases we show that it is equal to 3 for b 3 c 3 and 1 for d 3 a 3

generalized complex geometry generalized complex geometry encompasses complex and symplectic ge ometry as its extremal special cases we explore the basic properties of this geometry including its enhanced symmetry group elliptic deforma tion theory relation to poisson geometry and local structure theory we also dene and study generalized complex branes which interpolate be tween at bundles on lagrangian submanifolds and holomorphic bundles on complex submanifolds

identification of nonminimum phase fir systems using the third and fourth order cumulants an algorithm is proposed for ma system identification using the third and fourth order cumulants asymmetric non gaussian input and gaussian measurement noise are assumed simulation results show that the proposed algorithm is useful when the characteristics of noise are not known or when the snr is low

the quantum poincare birkhoff witt theorem we define and study a wide class of associative algebras in which the poincare birkhoff witt theorem is valid this class includes numerous quantum algebras which recently appeared

poisson co homology of polynomial poisson algebras in dimension four sklyanin s case abstract in this paper we compute the poisson co homology of a polynomial poisson structure given by two casimir polynomial functions which define a complete intersection with an isolated singularity

twisted poincare duality between poisson homology and poisson cohomology abstract a version of the twisted poincare duality is proved between the poisson homology and cohomology of a polynomial poisson algebra with values in an arbitrary poisson module the duality is achieved by twisting the poisson module structure in a canonical way which is constructed from the modular derivation in the case that the poisson structure is unimodular the twisted poincare duality reduces to the poincare duality in usual sense the main result generalizes the work of launois and richard 8 for the quadratic poisson structures and zhu 25 for the linear poisson structures

poisson deformations of symplectic quotient singularities abstract we establish a connection between smooth symplectic resolutions and symplectic deformations of a possibly singular affine poisson variety in particular let v be a finite dimensional complex symplectic vector space and g sp v a finite subgroup our main result says that the so called calogero moser deformation of the orbifold v g is in an appropriate sense a versal poisson deformation that enables us to determine the algebra structure on the cohomology h x c of any smooth symplectic resolution x v g multiplicative mckay correspondence we prove further that if g gl h is an irreducible weyl group and v h h then no smooth symplectic resolution of v g exists unless g is of types a b c

iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo contractive mappings in banach spaces abstract in this article we prove some new convergence theorems of the ishikawa and mann iteration sequences for strongly accretive and strongly pseudo contractive mappings by using the new inequality and the new approximation methods our main results improve and extend the corresponding results of j math anal appl 151 1990 453 461 proc amer math soc 120 1994 545 551 j math appl 192 1995 502 518 j math anal appl 174 1993 441 449 acta appl math 32 1993 183 196 nonlinear anal tma 24 1995 981 987 j math anal appl 178 1993 9 21 proc amer math soc 125 6 1997 1705 1709

identification of linear stochastic systems via second and fourth order cumulant matching the identification problem for time invariant single input single output linear stochastic systems driven by non gaussian white noise is considered the system is not restricted to be minimum phase and it is allowed to contain all pass components a least squares criterion that involves matching the second and the fourth order cumulant functions of the noisy observations is proposed knowledge of the probability distribution of the driving noise is not required an order determination criterion that is a modification of the akaike information criterion is also proposed strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are presented to illustrate the method

hochschild and cyclic homology of quantum groups for an arbitrary complex linear semisimple lie groupg we consider hopf algebras of the deformations of the formal and algebraic functions ong the hochschild and cyclic homology of these hopf algebras are computed when the value of the deformation parameter is generic

efficient closed form estimation of multivariate moving average processes using higher order statistics an improved algorithm is proposed for estimation of non gaussian nonminimum phase multivariate moving average ma processes using higher order cumulants this algorithm improves upon earlier results and contains development beyond existing algorithms it provides a closed form solution to estimating the ma parameter matrices up to a post multiplication by a permutation matrix and under certain assumptions eliminates the indeterminacy associated with scaling the algorithm is theoretically derived and tested via computer simulations in addition it is shown that this algorithm is computationally more efficient than the one proposed by tong inouye and liu see ibid vol 40 no 10 p 2547 2558 1992 finally the effect of imperfect input data on our algorithm is tested via simulations

homology and cohomology on generalized poisson manifolds the canonical homology of a generalized poisson manifold is introduced and the two spectral sequences associated with the periodic double complex are studied the generalized poisson cohomology is also discussed and a natural parity with the canonical homology is established the results hold for nambu poisson manifolds

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

gerstenhaber algebras and bv algebras in poisson geometry the purpose of this paper is to establish an explicit correspondence between various geometric structures on a vector bundle with some well known algebraic structures such as gerstenhaber algebras and bv algebras some applications are discussed in particular we find an explicit connection between the koszul brylinski operator and the modular class of a poisson manifold as a consequence we prove that poisson homology is isomorphic to poisson cohomology for unimodular poisson structures

convergence theorems of fixed points for asymptotically hemi pseudocontractive mappings in this paper the concept of asymptotically hemi pseudocontractive mapping in banach space which is a proper generalization of asymptotically pseudocontractive mapping with nonempty fixed point set as shown by an example is introduced some sufficient and necessary conditions on the strong convergence of the modified ishikawa and the modified mann iteration sequences with mean errors for uniformly l lipshitzian asymptotically hemi pseudocontractive mappings are presented

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

system reconstruction based on selected regions of discretized higher order spectra we consider the problem of system reconstruction from arbitrarily selected slices of the nth order output spectrum we establish that unique identification of the impulse response of a system can be performed up to a scalar and a circular shift based on any two one dimensional 1 d slices of the discretized nth order output spectrum n spl ges 3 as long as the distance between the slices and the grid size satisfy a simple condition for the special case of real systems one slice suffices for system reconstruction the ability to choose the slices to be used for reconstruction enables us to avoid regions of the nth order spectrum where the estimation variance is high or where the ideal polyspectrum is expected to be zero as is the case for bandlimited systems we show that the obtained system estimates are asymptotically unbiased and consistent we propose a mechanism for selecting slices that result in improved system estimates we also demonstrate via simulations the superiority in terms of estimation bias and variance of the proposed method over existing approaches in the case of bandlimited systems

strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings in the present paper we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex banach space requiring one member t in the family to be semi compact our results extend and improve some recent results

iterative solution of nonlinear equations with strongly accretive operators abstract let e be a real banach space with a uniformly convex dual suppose t e e is a strongly accretive map with bounded range such that for each e the equation tx has a solution in e it is proved that each of the two well known fixed point iteration methods the mann and ishikawa iteration methods under suitable conditions converges strongly to a solution of the equation tx furthermore our method shows that such a solution is necessarily unique explicit error estimates are given our results resolve in the affirmative an open problem j math anal appl 151 no 2 1990 460 and generalize important known results

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

on the cohomology of the lie algebra of hamiltonian vector fields abstract the work of gelfand and fuks concerning the cohomology of the lie algebra of all vector fields on a manifold is extended to the cohomology of the lie algebra of all hamiltonian vector fields on a symplectic manifold the case of an even dimensional algebraic torus is treated in detail

poisson cohomology of the affine plane abstract we compute the poisson cohomology of homogeneous poisson structures on the plane the singular locus of such a poisson structure consists of a family of lines passing through o and we show how the dimensions of the first and second cohomology groups are related to the weight of o as a singular point of

generalized double affine hecke algebras of rank 1 and quantized del pezzo surfaces abstract let d be a simply laced dynkin diagram of rank r whose affinization has the shape of a star i e d 4 e 6 e 7 e 8 to such a diagram one can attach a group g whose generators correspond to the legs of the affinization have orders equal to the leg lengths plus 1 and the product of the generators is 1 the group g is then a 2 dimensional crystallographic group g z l z 2 where l is 2 3 4 and 6 respectively in this paper we define a flat deformation h t q of the group algebra c g of this group by replacing the relations saying that the generators have prescribed orders by their deformations saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots which are deformation parameters the algebra h t q for d 4 is the cherednik algebra of type c c 1 which was studied by noumi sahi and stokman and controls askey wilson polynomials we prove that h t q is the universal deformation of the twisted group algebra of g and that this deformation is compatible with certain filtrations on c g we also show that if q is a root of unity then for generic t the algebra h t q is an azumaya algebra and its center is the function algebra on an affine del pezzo surface for generic q the spherical subalgebra e h t q e provides a quantization of such surfaces we also discuss connections of h t q with preprojective algebras and painleve vi

asymptotically optimal estimation of ma and arma parameters of non gaussian processes from high order moments a description is given of an asymptotically minimum variance algorithm for estimating the ma moving average and arma autoregressive moving average parameters of non gaussian processes from sample high order moments the algorithm uses the statistical properties covariances and cross covariances of the sample moments explicitly a simpler alternative algorithm that requires only linear operations is also presented the latter algorithm is asymptotically minimum variance in the class of weighted least squares algorithms

homologies of cubic artin schelter regular algebras abstract the hochschild homology of cubic artin schelter regular algebras of type a with generic coefficients is computed we follow the method used by van den bergh k theory 8 1994 213 230 in the quadratic case and consider these algebras as deformations of a polynomial algebra with remarkable poisson brackets a new morphism of resolutions is introduced the de rham cohomology cyclic and periodic cyclic homologies and the hochschild cohomology are also computed

hard lefschetz theorem for sasakian manifolds we prove that on a compact sasakian manifold m g of dimension 2n 1 for any 0 p n the wedge product with d defines an isomorphism between the spaces of harmonic forms n p m and n p 1 m therefore it induces an isomorphism between the de rham cohomology spaces h m and h m such isomorphism is proven to be independent of the choice of a compatible sasakian metric on a given contact manifold as a consequence an obstruction for a contact manifold to admit sasakian structures is found

homology of algebras of families of pseudodifferential operators abstract we compute the hochschild cyclic and periodic cyclic homology groups of algebras of families of laurent complete symbols on manifolds with corners we show in particular that the spectral sequence associated with hochschild homology degenerates at e 2 and converges to hochschild homology as a byproduct we identify the space of residue traces on fibrations by manifolds with corners in the process we prove some structural results about algebras of complete symbols on manifolds with corners

uniqueness of multiplicative determinants on elliptic pseudodifferential operators we describe all multiplicative determinants on the pathwise connected component of identity in the group of invertible classical pseudodifferential operators on a closed manifold that are continuous along continuous paths and the restriction to zero order operators of which is of class c1 this boils down to a description of all traces on zero order classical pseudodifferential operators which turn out to be linear combinations of the wodzicki residue w and leading symbol traces introduced in pr1 both of which are continuous consequently multiplicative determinants are parametrized by the residue determinant w87 sc and a new leading symbol determinant both of which are expressed in terms of a homogeneous component of the symbol of the logarithm of the operator

an algebraic index theorem for orbifolds abstract using the concept of a twisted trace density on a cyclic groupoid a trace is constructed on a formal deformation quantization of a symplectic orbifold an algebraic index theorem for orbifolds follows as a consequence of a local riemann roch theorem for such densities in the case of a reduced orbifold this proves a conjecture by fedosov schulze and tarkhanov finally it is shown how the kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem

system identification using a linear combination of cumulant slices a linear approach to identifying the parameters of a moving average ma model from the statistics of the output is presented first it is shown that under some constraints the impulse response of the system can be expressed as a linear combination of cumulant slices then this result is used to obtain a well conditioned linear method for estimating the ma parameters of a nongaussian process the linear combination of slices used to compute the ma parameters can be constructed from different sets of cumulants of different orders provided a general framework in which all the statistics can be combined it is not necessary to use second order statistics autocorrelation slice and therefore the proposed algorithm still provides consistent estimates in the presence of colored gaussian noise another advantage of the method is that while most linear methods give totally erroneous estimates if the order is overestimated the proposed approach does not require a previous estimation of the filter order the simulation results confirm the good numerical conditioning of the algorithm and its improvement in performance in comparison to existing methods

approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces in this paper we consider an ishikawa type iteration process with errors which converges to the unique common fixed point of a pair of contractive type mappings in complete generalized convex metric spaces furthermore we obtain the corresponding results in banach spaces our results extend and generalize many known results

approaches of fir system identification with noisy data using higher order statistics the problem of estimating the parameters of a moving average model from the cumulant statistics of the noisy observations of the system output is discussed the system is driven by an independently identically distributed nongaussian sequence that is not observed the noise is additive and may be colored and nongaussian following some existing linear parametric approaches to this problem a linear method and a modification to an existing linear method are proposed for consistent parameter estimation in measurement noise under the assumption that the system order is known both recursive closed form and batch least squares versions of the parameter estimators are presented the existing and the proposed linear methods utilize only a partial set of the relevant output statistics this restriction being necessary to obtain a linear estimator whereas there exist nonlinear method that exploit a much larger set of output statistics a simulation example where two existing linear methods and the two new methods are compared to two existing nonlinear methods is presented

a new linear quotient of c 4 admitting a symplectic resolution we show that the quotient c4 g admits a symplectic resolution for g q 8 times bf z 2 d 8 sf sp 4 bf c here q8 is the quaternionic group of order eight and d8 is the dihedral group of order eight and g is the quotient of their direct product which identifies the nontrivial central elements id of each it is equipped with the tensor product representation bf c 2 boxtimes bf c 2 cong bf c 4 this group is also naturally a subgroup of the wreath product group q 8 2 rtimes s 2 sf sp 4 bf c we compute the singular locus of the family of commutative spherical symplectic reflection algebras deforming c4 g we also discuss preliminary investigations on the more general question of classifying linear quotients v g admitting symplectic resolutions

poisson co homology and isolated singularities abstract to each polynomial f x y z is associated a poisson structure on f 3 a surface and a poisson structure on this surface when is weight homogeneous with an isolated singularity we determine the poisson cohomology and homology of the two poisson varieties obtained

ma parameter estimation and cumulant enhancement this paper addresses the problem of estimating the parameters of a moving average ma model from either only third or fourth order cumulants of the noisy observations of the system output the system is driven by an independent and identically distributed non gaussian sequence that is not observed the unknown model parameters are obtained using a batch least squares method recursive methods are also developed and used to claim the uniqueness of the batch least squares solutions a novel technique for the enhancement of third order cumulants of ma processes is introduced this new technique is based on the concept of composite property mappings and helps reduce the variance of the estimates of third or fourth order cumulants of ma processes simulation results are presented that demonstrate the performance of the new methods and compare them with a range of existing techniques

hochschild co homology of differential operator rings abstract we show that the hochschild homology of a differential operator k algebra e a fu g is the homology of a deformation of the chevalley eilenberg complex of g with coefficients in m formula b moreover when a is smooth and k is a characteristic zero field we obtain a type of hochschild kostant rosenberg theorem for these algebras when a k our complex reduces to the one obtained by c kassel 1988 invent math 91 221 251 for the homology of filtrated algebras whose associated graded algebras are symmetric algebras in the last section we give similar results for the cohomology

on chidume s open questions and approximate solutions of multivalued strongly accretive mapping equations in banach spaces abstract some new convergence theorems of the ishikawa iteration process for multi valued pseudo contractive mappings and multi valued accretive mappings are obtained which affirmatively answer the open questions put forth by 4

examples of non kahler hamiltonian circle manifolds with the strong lefschetz property abstract in this paper we construct six dimensional compact non kahler hamiltonian circle manifolds which satisfy the strong lefschetz property themselves but nevertheless have a non lefschetz symplectic quotient this provides the first known counterexamples to the question whether the strong lefschetz property descends to the symplectic quotient we also give examples of hamiltonian strong lefschetz circle manifolds which have a non lefschetz fixed point submanifold in addition we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong lefschetz manifold we then use it to show the existence of lefschetz four manifolds with non lefschetz finite covering spaces

duality and modular class of a nambu poisson structure in this paper we introduce cohomology and homology theories for nambu poisson manifolds also we study the relation between the existence of a duality for these theories and the vanishing of a particular nambu poisson cohomology class the modular class the case of a regular nambu poisson structure and some singular examples are discussed

cyclic cocycles on deformation quantizations and higher index theorems abstract we construct a nontrivial cyclic cocycle on the weyl algebra of a symplectic vector space using this cyclic cocycle we construct an explicit local quasi isomorphism from the complex of differential forms on a symplectic manifold to the complex of cyclic cochains of any formal deformation quantization thereof we give a new proof of nest tsygan s algebraic higher index theorem by computing the pairing between such cyclic cocycles and the k theory of the formal deformation quantization furthermore we extend this approach to derive an algebraic higher index theorem on a symplectic orbifold as an application we obtain the analytic higher index theorem of connes moscovici and its extension to orbifolds

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

algebraic index theorem we prove the atiyah singer index theorem where the algebra of pseudodifferential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold

harmonic cohomology of symplectic manifolds abstract mathieu math helv 70 1995 1 introduced a canonic filtration in the de rham cohomology of a symplectic manifold and proved that the middle filtration space is the space of harmonic cohomology classes we give an interpretation of the other filtration spaces prove a kunneth theorem for harmonic cohomology prove poincare duality for harmonic cohomology and show how surjectivity of certain lefschetz type mappings is related to properties of the filtration for a closed symplectic manifold m we also introduce symplectic invariants l m l 0 and show l 0 l m sign m if m is of dimension 2n with n even

extension of the matrix bartlett s formula to the third and fourth order and to noisy linear models with application to parameter estimation this paper focuses on the extension of the asymptotic covariance of the sample covariance denoted bartlett s formula of linear processes to thirdand fourth order sample cumulant and to noisy linear processes closed form expressions of the asymptotic covariance and cross covariance of the sample second third and fourth order cumulants are derived in a relatively straightforward manner thanks to a matrix polyspectral representation and a symbolic calculus akin to a high level language as an application of these extended formulae we underscore the sensitivity of the asymptotic performance of estimated arma parameters by an arbitrary third or fourth order based algorithm with respect to the signal to noise ratio the spectra of the linear process and the colored additive noise

new results on fir system identification using higher order statistics the problem of estimating the parameters of a moving average model from the cumulant statistics of the noisy observations of the system output is considered the system is driven by an i i d independent and identically distributed non gaussian sequence that is not observed the noise is additive and may be colored and non gaussian re parametrization of an existing linear method and a modification to it are discussed simulation results show a distinct improvement in the numerical conditioning of both the reparametrized algorithm and its modification for the noisefree case for the case of i i d noise the reparametrized algorithm shows a marked degradation in performance whereas its modification degrades far more gracefully

fir system identification using higher order statistics alone this paper focuses on fir system identification in gaussian arma noise using higher order cumulants alone two new types of cumulant based normal equations are established and two algorithms are proposed for ma parameter estimation simulations verify the high performance of the new developments

sample cumulants of stationary processes asymptotic results in this paper we present the formulas of the covariances of the second third and fourth order sample cumulants of stationary processes these expressions are then used to obtain the analytic performance of fir system identification methods as a function of the coefficients and the statistics of the input sequence the lower bound in the variance is also compared for different sets of sample statistics to provide insight about the information carried by each sample statistic finally the effect that the presence of noise has on the accuracy of the estimates is studied analytically the results are illustrated graphically with plots of the variance of the estimates as a function of the parameters or the signal to noise ratio monte carlo simulations are also included to compare their results with the predicted analytic performance

the lefschetz property formality and blowing up in symplectic geometry in this paper we study the behaviour of the lefschetz property under the blow up construction we show that it is possible to reduce the dimension of the kernel of the lefschetz map if we blow up along a suitable submanifold satisfying the lefschetz property we use this together with results about massey products to construct compact nonformal symplectic manifolds satisfying the lefschetz property

deformations of holomorphic pseudo symplectic poisson manifolds abstract we prove unobstructed deformations for compact kahlerian even dimensional poisson manifolds whose poisson tensor degenerates along a divisor with mild singularities examples include hilbert schemes of del pezzo surfaces

nambu jacobi and generalized jacobi manifolds the geometry of nambu jacobi and generalized jacobi manifolds is studied a large collection of examples is given the characteristic distribution generated by the hamiltonian vector fields on a nambu jacobi manifold is proved to be completely integrable and the induced geometrical structure of the leaves of the corresponding generalized foliation is ellucidated

cohomology and hodge theory on symplectic manifolds iii arxiv 1402 0427v2 math sg 2 may 2014 cohomology and hodge theory on symplectic manifolds iii chung jun tsai li sheng tseng and shing tung yau february 3 2014 abstract we introduce filtered cohomologies of differential forms on symplectic manifolds they generalize and include the cohomologies discussed in paper i and ii as a subset the filtered cohomologies are finite dimensional and can be associated with differential elliptic complexes algebraically we show that the filtered cohomologies give a two sided resolution of lefschetz maps and thereby they are directly related to the kernels and cokernels of the lefschetz maps we also introduce a novel non associative product operation on differential forms for symplectic manifolds this product generates an a algebra structure on forms that underlies the filtered cohomologies and gives them a ring structure as an application we demonstrate how the ring structure of the filtered cohomologies can distinguish different symplectic four manifolds in the context of a circle times a fibered three manifold contents 1 introduction 2 preliminaries operations on differential forms 10 filtered forms and differential operators 14 short exact sequences 16

noncommutative kahler structures on quantum homogeneous spaces abstract building on the theory of noncommutative complex structures the notion of a noncommutative kahler structure is introduced in the quantum homogeneous space case many of the fundamental results of classical kahler geometry are shown to follow from the existence of such a structure allowing for the definition of noncommutative lefschetz hodge kahler dirac and laplace operators quantum projective space endowed with its heckenberger kolb calculus is taken as the motivating example the general theory is then used to show that the calculus has cohomology groups of at least classical dimension

the graded jacobi algebras and co homology jacobi algebroids i e jacobi versions of lie algebroids are studied in the context of graded jacobi brackets on graded commutative algebras this unifies various concepts of graded lie structures in geometry and physics a method of describing such structures by classical lie algebroids via certain gauging in the spirit of e witten s gauging of the exterior derivative is developed one constructs a corresponding cartan differential calculus graded commutative one in a natural manner this in turn gives canonical generating operators for triangular jacobi algebroids one gets in particular the lichnerowicz jacobi homology operators associated with classical jacobi structures courant jacobi brackets are obtained in a similar way and used to define an abstract notion of a courant jacobi algebroid and dirac jacobi structure