character generators for elements of finite order in simple lie groups a1 a2 a3 b2 and g2 elements of finite order in the compact simple lie groups su 2 su 3 su 4 sp 4 or o 5 and g 2 are considered we provide the characters of the elements on irreducible representations of lie groups by assigning appro priate numerical values to the variables on which the characters of representations of the lie group depend in this way we specialize generating functions for the characters of the representations of the lie groups to the generating functions for characters of the elements of finite order particular attention is paid to rational elements all of whose characters are integers they are listed and the generating functions for their characters are obtained in a simplified form from which the characters can be read gaussian elements are also studied in detail their characters are complex valued with integer real and imaginary parts

grading refinements in the contractions of lie algebras and their invariants all mutually inequivalent toroidal gradings of the lie algebra are constructed each of them provides several different graded contractions to other eight dimensional lie algebras these can be either continuous or discrete the continuous ones are related to generalized wigner inonu contractions the behaviour of casimir operators under the graded contractions is studied and the casimir and generalized casimir operators of the contracted lie algebras are presented

fast recursion formula for weight multiplicities the purpose of this note is to describe and prove a fast recursion formula for computing multiplicities of weights of finite dimensional representations of simple lie algebras over c until now information about weight multiplicities for all but some special cases 1 2 has had to be found from the recursion formulas of freudenthal 3 or racah 4 typically these formulas become too laborious to use for hand computations for ranks 5 and dimensions 1 0 0 and for ranks 10 and dimensions 10 on a large computer 5 6 with the proposed method the multiplicities can routinely be calculated even by hand for dimensions far exceeding these as an example we present a summary of calculations 7 of all multiplicities in the first sixteen irreducible representations of es let be a semisimple lie algebra over c with root system a and weyl group w relative to a cartan subalgebra let a be the positive roots with respect to some ordering and ii at a the set of simple roots let q and p be the root and weight lattices respectively spanning the real vector space f c if x c p we denote by x the set of dominant elements of x relative to n let m be an irreducible module with highest weight a and weight system 2 an important feature of the approach is the direct determination of 2 without computing outside the dominant chamber since every w orbit is represented by one weight x 2 of the same multiplicity it suffices to compute such x s the recursion formula for computing the multiplicities is a modification proposition 4 of the freudenthal formula in which the weyl group has been exploited to collapse it as much as possible after describing the procedure we present the e example finally the necessary proofs are given

underdetermined order recursive least squares adaptive filtering the concept and algorithms underdetermined recursive least squares urls adaptive filtering is introduced in particular the urls algorithm is derived and shown to be a direct consequence of the principle of minimal disturbance by exploiting the hankel structure of the filter input matrix the fast transversal filter ftf version of the urls algorithm urls ftf is derived including sliding window and growing window types the computational complexity is reduced to o n o m where n is the adaptive filter length and m is the order of the urls algorithm in addition the efficient urls eurls algorithm which does not compute the filter coefficients explicitly thereby significantly reducing the computational load is presented some earlier adaptive algorithms such as the averaged lms filtered x lms and fast conjugate gradient are shown to be suboptimal approximations of the urls algorithm instrumental variable approximations are also discussed the urls algorithm has a whitening effect on the input signal which provides immunity to the eigenvalue spread of the input signal correlation matrix although the algorithm is sensitive to observation noise it has good tracking characteristics and tradeoffs can be found by tuning the step size the utility of the urls algorithms in its basic form and ftf realization depends heavily on the practical applicability of the mth order sliding window estimate of the covariance matrix and mth order ptf relations the feasibility of the urls family in practical applications is demonstrated in channel equalization and acoustic echo cancellation

generating functions for g2 characters and subgroup branching rules the g2 character generator is given with its help generating functions are derived for branching rules for g2 irreducible representations reduced according to its maximal semisimple subgroups

a direction set based algorithm for least squares problems in adaptive signal processing abstract a fast algorithm has been developed for solving a class of least squares problems arising in adaptive signal processing the algorithm is based on the powell and zangwill direction set method for unconstrained minimization problems and is designed so as to fully take advantage of the special structure of the adaptive least squares als problems it is a fast algorithm because it requires only o n multiplications for each system update where n is the dimension of the problem the algorithm has been implemented and applied to applications in signal processing computer simulation results have shown that the algorithm is stable and converges fast often with a rate which is comparable to that of the known cg and rls algorithm the convergence behavior of the algorithm is studied in detail in this paper the algorithm is shown to converge linearly for adaptive least squares problems in general and its rate of convergence can be faster than linear for some applications a computational procedure is also designed to generate a set of near conjugate directions as initial directions to accelerate the convergence

general charge conjugation operators in simple lie groups a description of particular elements charge conjugation operators found in any compact simple lie group k is presented such elements ri transform a physical state weight vector of a basis of a representation space into others with opposite charge ith component of the weight sometime changing also the sign of the state it is demonstrated that exploitation of these elements and the finite subgroup n of k generated by them offer new powerful methods for computing with representations of the lie group their application to construction of bases in representation spaces is considered in detail it represents a completely new direction to the problem

the block processing ftf adaptive algorithm a new block type adaptive filtering algorithm is presented this new block adaptive filter differs from the frequency domain block adaptive filters of ferrara 1980 and of clark mitra and parker 1980 in that the new method applies a deterministic time domain least squares criteria within each of the data blocks information is carried from block to block via a weighted initial condition this new block fast transversal filters bftf algorithm is a numerically stable algorithm and can also be used to perform efficient least squares system identification on any one data block in which case it shows a moderate computational advantage over the previous most efficient single data block algorithms of morf et al 1977 of marple 1981 and of kalouptsidis manolakis and carayannis 1984 1985 mechanisms for tracking and varying block length from block to block are also presented and evaluated finally we indicate how the new algorithm could be pipelined for maximum throughput with delay proportional to the number of parameters after computation of the sample correlation lags

a numerically stable fast newton type adaptive filter based on order recursive least squares algorithm this paper presents a numerically stable fast newton type adaptive filter algorithm two problems are dealt with in the paper first we derive the proposed algorithm from an order recursive least squares algorithm the result of the proposed algorithm is equivalent to that of the fast newton transversal filter fntf algorithm however the derivation process is different instead of extending a covariance matrix of the input based on the min max and the max min criteria the derivation shown in this paper is to solve an optimum extension problem of the gain vector based on the information of the mth order forward or backward predictor the derivation provides an intuitive explanation of the fntf algorithm which may be easier to understand second we present stability analysis of the proposed algorithm using a linear time variant state space method we show that the proposed algorithm has a well analyzable stability structure which is indicated by a transition matrix the eigenvalues of the ensemble average of the transition matrix are proved all to be asymptotically less than unity this results in a much improved numerical performance of the proposed algorithm compared with the combination of the stabilized fast recursive least squares sfrls and the fntf algorithms computer simulations implemented by using a finite precision arithmetic have confirmed the validity of our analysis

efficient least squares fir system identification if finite impulse response fir system identification is performed by minimizing the squared error between the measured system output and an estimate from an fir system output a set of least squares normal equations to be solved for the fir system coefficients is obtained if the assumed fir system is of duration m samples the usual solution for the m least squares simultaneous equations requires a number of computational operations proportional to m3and storage of normal equation coefficients proportional to m2 the set of normal equations has an underlying structure however that can be exploited to yield a solution with computational operations proportional to m2and storage proportional to m such an efficient algorithmic solution is presented here

fast design of multichannel fir least squares filters with optimum lag this paper is mainly concerned with the efficient design of optimum lag fir least squares filters these filters result when the minimization of the total mean square error encompasses a time shift between the input signal and the desired response the solution of this problem leads to a family of normal systems of equations whose associated matrix is the same while the right hand side members are parametrized by the lag ranging within a specified interval the fast algorithm derived here for the determination of the optimum lag filter provides the solutions of the above family of systems by step up step down levinson like order recursions coupled with time updating kalman like relations and offers a recursive error capability as well this is achieved by exploiting the near to toeplitz structure of the matrix and a certain shift invariance property the right hand side members possess finally motivated by the optimum lag problem systems of equations with near to toeplitz parameters are considered and a fast algorithm is developed the proposed schemes find important applications in seismic signal processing system identification economic forecasting etc

simplified newton type adaptive estimation algorithms a new adaptive estimation algorithm is presented it is the result of a combination of the lms and the fast newton transversal filters fntf class the main characteristic of the proposed algorithm is its improved convergence rate as compared to lms for cases where it is known that lms behaves poorly this improved characteristic is achieved in expense of a slight increase in the computational complexity while the overall algorithmic structure is very simple lms type the proposed algorithm seems also to compare relatively well against rls and fntf

clebsch gordan coefficients for su 5 su 3 su 2 u 1 theories the clebsch gordan coefficients are calculated for the following tensor products of su 5 representations 5 5 5 10 5 10 15 5 15 5 10 10 5 5 10 10 5 24 and 10 24 each case is calculated twice once in a weight vector basis independent of any semisimple subgroup the second time in a basis which refers to su 3 su 2 u 1 su 5

generating functions and elementary young tableaux when constructing polynomial bases for group representations one is led naturally to consider a stretched product of states elementary multiplets are states that cannot be expressed as the stretched product of any other two states and they can be identified with terms occurring in certain generating functions in this paper the authors define an analogous stretched product of young tableaux together with elementary tableaux these may be used in a manner similar to elementary multiplets to construct generating functions they consider several examples where this method can be applied and in particular give new large n rank free branching rule generating functions for the group subgroup pairs su n su m contained in implied by su n m first four labels non zero so n contained in implied by su n first three labels non zero and sp 2n contained in implied by su 2n first five labels non zero this method of finding these generating functions uses the theory of grobner bases which allows the authors to make precise the notion of compatibility relations or forbidden products of elementary tableaux

computation of character decompositions of class functions on compact semisimple lie groups a new algorithm is described for splitting class functions of an arbitrary semisimple compact lie group k into sums of irreducible characters the method is based on the use of elements of finite order efo in k and is applicable to a number of problems including decompositions of tensor products and various symmetry classes of tensors as well as branching rules in group subgroup reductions the main feature is the construction of a decomposition matrix d computed once and for all for a given range of problems and for a given k which then reduces any particular splitting to a simple matrix multiplication determination of d requires selection of a suitable set s of conjugacy classes of efo representing a finite subgroup of a maximal torus t of k and the evaluation of weyl group orbit sums on s in fact the evaluation of d can be coupled with the evaluation of the orbit sums in such a way as to greatly enhance the efficiency of the latter the use of the method is illustrated by some extensive examples of tensor product decompositions in e6 modular arithmetic allows all computations to be performed exactly

a step by step quasi newton algorithm in the frequency domain and its application to adaptive channel equalization in this paper a new efficient adaptive filtering algorithm belonging to the quasi newton qn family is proposed in the new algorithm the involved inverse hessian matrix is approximated by a proper expansion consisting of powers of a toeplitz matrix due to this formulation the algorithm can be implemented in the frequency domain fd using the fast fourier transform fft efficient recursive relations for the frequency domain quantities updated on a step by step basis have been derived the proposed algorithm turns out to be particularly suitable for adaptive channel equalization in wireless burst transmission systems based on this approach new adaptive linear equalization le and decision feedback equalization dfe algorithms have been developed these algorithms enjoy the combined advantages of qn formulation and fd implementation exhibiting faster convergence rate than their stochastic gradient counterparts and less computational complexity as compared with other newton type algorithms

poisson structures on moduli spaces of sheaves over poisson surfaces we introduce and study the notion of poisson surface we prove that the choice of a poisson structure on a surfaces canonically determines a poisson structure on the moduli space of stable sheaves ons this result generalizes previous results obtained by mukai 14 for abelian ork3 surfaces and by tyurin 16

kirwan surjectivity for quiver varieties for algebraic varieties defined by hyperkahler or more generally algebraic symplectic reduction it is a long standing question whether the hyperkahler kirwan map on cohomology is surjective we resolve this question in the affirmative for nakajima quiver varieties we also establish similar results for other cohomology theories and for the derived category our proofs use only classical topological and geometric arguments

superfast approximative implementation of the iaa spectral estimate in this correspondence we develop superfast approximative one dimensional algorithms for the computationally efficient implementation of the recent iterative adaptive approach iaa spectral estimate the proposed methods are based on rewriting the iaa algorithm with suitable gohberg semencul representations solving the resulting linear systems of equations using the preconditioned conjugate gradient method where a novel preconditioning is applied using an incomplete factorization of the toeplitz matrix numerical simulations illustrate the efficiency of both the proposed preconditioning as well as the overall algorithm offering a computational reduction of up to two orders of magnitude as compared to our recently proposed efficient and exact iaa implementation

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

fast algorithms for discrete time wiener filters with optimum lag in many applications including geophysical signal processing and system identification the computation of a fir wiener filter corresponding to the optimum lag between the input signal and the desired response or of an optimum prediction distance predictor are often required these problems lead to the solution of a family of toeplitz systems of equations having the same associated matrix but right hand side vectors which are shifted versions of each other a very efficient method for the solution of the optimum lag problem is the well known simpson s sideways recursions the purpose of this paper is to introduce two new algorithms for the efficient computation of the optimum lag wiener filter as well as the optimum prediction distance predictor their main characteristic is a coupled step down step up recursion which takes full advantage of both the toeplitz nature of the matrix and the shifted structure of the right hand side vectors the proposed algorithms are featured by increased speed they are about twice as fast as simpson s scheme and computational simplicity in addition they provide recursive error computation capability and give further insight into the problem

a fast newton multichannel algorithm for decision feedback equalization fast newton transversal filters fntf are a new class of adaptive algorithms unifying nlms and fast rls this is achieved by allowing the algorithm to exploit a priori information about the associated predictors order this note extends fntf to the multichannel case and demonstrates the applicability of the resulting algorithm to decision feedback equalization

polynomial states for su 3 and so 5 in a demazure tits basis the authors construct basis states for su 3 and for so 5 that are polynomials in the states of the fundamental representations they are reduced according to the finite demazure tits subgroup which acts on basis states in the same manner that the weyl group acts on weights

the demazure tits subgroup of a simple lie group the demazure tits subgroup of a simple lie group g is the group of invariance of clebsch gordan coefficients tables assuming an appropriate choice of basis the structure of the demazure tits subgroups of an bn cn dn and g2 is described orbits of the permutation action of the dt group in any irreducible finite dimensional representation space of a2 c2 and g2 are decomposed into the sum of irreducible representations of the dt group

vertex algebras and the cohomology ring structure of hilbert schemes of points on surfaces using vertex algebra techniques we determine a set of generators for the cohomology ring of the hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers

the kage rls algorithm a new fast recursive least squares rls algorithm the kalman gain estimator kage is introduced by making use of rls interpolation as well as prediction the algorithm generates the transversal filter weights without suffering the poor numerical attributes of the fast transversal filter ftf algorithm the kalman gain vector is generated at each time step in terms of interpolation residuals the interpolation residuals are calculated in an order recursive manner for an n sup th order problem the procedure requires o nlog sub 2 n operations per iteration this is achieved via a divide and conquer approach computer simulations suggest that the new algorithm is numerically robust running successfully for many millions of iterations

the state labeling problem a universal solution a new method is proposed for labeling a basis for any irreducible representation with top weight of a simple lie algebra la it has two advantages over gel fand zetlin patterns i being exactly the same for all la s both exceptional and classical and ii providing labels that are much more compact thus it may prove useful in discussing large representations such as those e8 e8 that occur in superstring theory the method makes essential use of the weyl group and is based on a theorem that associates to each weight a symmetric matrix with integer coefficients whose rank equals the multiplicity of the weight

a direction set based algorithm for adaptive filtering a new algorithm is developed for adaptive filtering applications this algorithm is based on a direction set method and has a computational complexity of o n for each update of the system the method exploits the structure of the objective function and maintains a set of near conjugate directions with respect to the hessian this algorithm has a rapid rate of convergence that is comparable with that of the well known rls method the performance of the algorithm is illustrated with adaptive filtering applications

integral operators and integral cohomology classes of hilbert schemes the methods of integral operators on the cohomology of hilbert schemes of points on surfaces are developed they are used to establish integral bases for the cohomology groups of hilbert schemes of points on a class of surfaces and conjecturally for all simply connected surfaces

orbifold cohomology for global quotients let x be an orbifold that is a global quotient of a manifold y by a finite group g we construct a noncommutative ring h sp ast y g with a g action such that h sp y g sp g is the orbifold cohomology ring of x defined by w chen and y ruan cr when y s sp n with s a surface with trivial canonical class and g mathfrak s sb n we prove that a small modification of the orbifold cohomology of x is naturally isomorphic to the cohomology ring of the hilbert scheme s sp n computed by m lehn and c sorger ls2

efficient recursive in order least squares fir filtering and prediction this paper is concerned with the efficient determination of the optimum in the least squares sense fir filter on the basis of data samples of the input and desired response signals by procedures recursive in the filter order this situation typically arises when no a priori statistics are available and the system order is not known the general multiinput multioutput multichannel case is considered here and a fast algorithm is presented requiring for single channel signals approximately 2s 15m multiplications mps per order m s being the number of samples in the special case of linear prediction it calls for about s 12m mps hence it offers a computational reduction of 5m and 2m mps in comparison to the methods of marple 1 and morf et al 2 respectively additionally the proposed scheme is inherently symmetric and is suited very well to initialization of fast sequential algorithms as well as algorithms searching for the optimum lag filter

generators for the cohomology ring of the moduli space of rank 2 higgs bundles the moduli space of stable vector bundles on a riemann surface is smooth when the rank and degree are coprime and is diffeomorphic to the space of unitary connections of central constant curvature a classic result of newstead and atiyah and bott asserts that its rational cohomology ring is generated by the universal classes that is by the kunneth components of the chern classes of the universal bundle this paper studies the larger non compact moduli space of higgs bundles as introduced by hitchin and simpson with values in the canonical bundle k this is diffeomorphic to the space of all connections of central constant curvature whether unitary or not the main result of the paper is that in the rank 2 case the rational cohomology ring of this space is again generated by universal classes the spaces of higgs bundles with values in k n for n 0 turn out to be essential to the story indeed we show that their direct limit has the homotopy type of the classifying space of the gauge group and hence has cohomology generated by universal classes

integral generators for the cohomology ring of moduli spaces of sheaves over poisson surfaces abstract let m be a smooth and compact moduli space of stable coherent sheaves on a projective surface s with an effective or trivial anti canonical line bundle we find generators for the cohomology ring of m with integral coefficients when s is simply connected and a universal sheaf e exists over s m then its class e admits a kunneth decomposition as a class in the tensor product k top 0 s k top 0 m of the topological k rings the generators are the chern classes of the kunneth factors of e in k top 0 m the general case is similar

fast newton transversal filters a new class of adaptive estimation algorithms a class of adaptive algorithms for the estimation of fir finite impulse response transversal filters is presented the main characteristic of this class is the fast computation of the gain vector needed for the adaptation of the transversal filters the method for deriving these algorithms is based on the assumption that the input signal is autoregressive of order m where m can be much smaller than the order of the filter to be estimated under this assumption the covariance matrix of the input signal is estimated by extending in a min max way the m order sample covariance matrix this estimate can be regarded as a generalization of the diagonal covariance matrix used in lms and leads to an efficient computation of the gain needed for the adaptation the new class of algorithms contains the lms and the fast versions of ls as special cases the complexity changes linearly with m starting from the complexity of the lms for m 0 and ending at the complexity of the fast versions of ls

study of the transient phase of the forgetting factor rls we investigate the convergence properties of the forgetting factor rls algorithm in a stationary data environment using the settling time as our performance measure we show that the algorithm exhibits a variable performance that depends on the particular combination of the initialization and noise level specifically when the observation noise level is low high snr rls when initialized with a matrix of small norm it has an exceptionally fast convergence convergence speed decreases as we increase the norm of the initialization matrix in a medium snr environment the optimum convergence speed of the algorithm is reduced as compared with the previous case however rls becomes more insensitive to initialization finally in a low snr environment we show that it is preferable to initialize the algorithm with a matrix of large norm

square root covariance ladder algorithms square root normalized ladder algorithms provide an efficient recursive solution to the problem of multichannel autoregressive model fitting a simplified derivation of the general update formulas for such ladder forms is presented and is used to develop the growing memory and sliding memory covariance ladder algorithms new ladder form realizations for the identified models are presented leading to convenient methods for computing the model parameters from estimated reflection coefficients a complete solution to the problem of possible singularity in the ladder update equations is also presented

a pipelined structure for qr adaptive ls system identification a novel systolic array for ls system identification based on qr factorization via givens rotations is proposed the back substitution step is circumvented and the structure is fully pipelineable thus the method is appropriate for continuous sample by sample mode adaptive operation a modification of this structure is also suggested which is suitable for a wide range of linear algebraic operations and is solely based on givens rotations

fine gradings of o 5 c sp 4 c and of their real forms there are three fine gradings of the simple lie algebra of type b2 over the complex number field they provide a basic information about the structure of the algebra in the paper an explicit description of all fine gradings is given in terms of the four dimensional symplectic sp 4 c and five dimensional orthogonal o 5 c representations of the algebra in addition the real forms of b2 are considered it is shown which of the fine gradings survive the restriction to each of the real forms these results should be useful in defining various sets of additive quantum numbers for systems with such symmetries for systematic study of grading preserving contractions of this lie algebra and generally for choosing bases which reflect structural properties of the lie algebra

interference rejection in pn spread spectrum systems with ls linear phase fir filters the effects of a narrowband interference present in a pseudonoise pn spread spectrum system can be minimized by using digital whitening techniques a new efficient block ls algorithm for the design of an fir filter with linear phase is derived and used as a whitening filter simulations are carried out to demonstrate the effectiveness of the ls optimum linear phase filter in suppressing a narrowband interference in a pn spread spectrum system comparisons to previously used methods are made the simulations showed an improvement in the output snr on the order of 4 5 db over already existing schemes

pairwise optimal weight realization acceleration technique for set theoretic adaptive parallel subgradient projection algorithm the adaptive parallel subgradient projection psp algorithm was proposed in 2002 as a set theoretic adaptive filtering algorithm providing fast and stable convergence robustness against noise and low computational complexity by using weighted parallel projections onto multiple time varying closed half spaces in this paper we present a novel weighting technique named pairwise optimal weight realization power for further acceleration of the adaptive psp algorithm a simple closed form formula is derived to compute the projection onto the intersection of two closed half spaces defined by a triplet of vectors using the formula inductively the proposed weighting technique realizes a good direction of update the resulting weights turn out to be pairwise optimal in a certain sense the proposed algorithm has the inherently parallel structure composed of q primitive functions hence its total computational complexity o qrn is reduced to o rn with q concurrent processors r a constant positive integer numerical examples demonstrate that the proposed technique for r 1 yields significantly faster convergence than not only adaptive psp with uniform weights affine projection algorithm and fast newton transversal filters but also the regularized recursive least squares algorithm

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

clebsch gordan coefficients for su 5 unification models the clebsch gordan coefficients for the product 1001 1001 where 1001 is the adjoint representation of su 5 with respect to the group basis and the subgroup basis in the reduction su 5 su 3 su 2 u 1 are computed one of the basic tools in this computation is the exhaustive use of the verma algorithm to find bases for the weight subspaces of dimension higher than 1 it allows for the construction of bases in a systematic way by using the so called verma inequalities only the coefficients for the dominant weights are calculated the other ones can be obtained by using the elements of finite order charge conjugation operators of su 5

finite precision analysis of a covariance algorithm for least squares fir filtering and ar modeling a numerically stable fast order recursive algorithm for solving the covariance problem in signal modeling is described the propagation of finite arithmetic errors as well as data acquisition errors is studied in detail first linearization of the main algorithmic recursions is carried out then a suitable transformation converts the resulting state equations of the accumulated errors into their residual form subsequently bounds for the residuals are computed the derivation of these bounds depends heavily on the levinson type structure of the algorithm and the low displacement rank of the problem the main result is that the algorithm is weakly numerically stable the proposed order recursive algorithm is subsequently utilized as a block adaptive method its performance is also demonstrated by long run simulations

the cup product of hilbert schemes for k3 surfaces to any graded frobenius algebra a we associate a sequence of graded frobenius algebras a n so that there is canonical isomorphism of rings h x 2 n h x n 2n for the hilbert scheme x n of generalised n tuples of any smooth projective surface x with numerically trivial canonical bundle

normalized sliding window constant modulus and decision directed algorithms a link between blind equalization and classical adaptive filtering by minimizing a deterministic criterion of the constant modulus cm type or of the decision directed dd type we derive normalized stochastic gradient algorithms for blind linear equalization be of qam systems these algorithms allow us to formulate cm and dd separation principles which help obtain a whole family of cm or dd be algorithms from classical adaptive filtering algorithms we focus on the algorithms obtained by using the affine projection adaptive filtering algorithm apa their increased convergence speed and ability to escape from local minima of their cost function make these algorithms very promising for be applications

fast lcmv based methods for fundamental frequency estimation recently optimal linearly constrained minimum variance lcmv filtering methods have been applied to fundamental frequency estimation such estimators often yield preferable performance but suffer from being computationally cumbersome as the resulting cost functions are multimodal with narrow peaks and require matrix inversions for each point in the search grid in this paper we therefore consider fast implementations of lcmv based fundamental frequency estimators exploiting the estimators inherently low displacement rank of the used toeplitz like data covariance matrices using as such either the classic time domain averaging covariance matrix estimator or if aiming for an increased spectral resolution the covariance matrix resulting from the application of the recent iterative adaptive approach iaa the proposed exact implementations reduce the required computational complexity with several orders of magnitude but as we show further computational savings can be obtained by the adoption of an approximative iaa based data covariance matrix estimator reminiscent of the recently proposed quasi newton iaa technique furthermore it is shown how the considered pitch estimators can be efficiently updated when new observations become available the resulting time recursive updating can reduce the computational complexity even further the experimental results show that the performances of the proposed methods are comparable or better than that of other competing methods in terms of spectral resolution finally it is shown that the time recursive implementations are able to track pitch fluctuations of synthetic as well as real life signals

moduli spaces of stable sheaves on abelian surfaces in this paper we consider basic problems on moduli spaces of stable sheaves on abelian surfaces our main assumption is the primitivity of the associated mukai vector we determine the deformation types albanese maps bogomolov factors and their weight 2 hodge structures we also discuss the deformation types of moduli spaces of stable sheaves on k3 surfaces

a new family of concurrent algorithms for adaptive volterra and linear filters a novel idea for introducing concurrency in least squares ls adaptive algorithms by sacrificing optimality has been proposed the resultant class of algorithms provides schemes to fill the wide gap in the convergence rates of ls and stochastic gradient sg algorithms it will be particularly useful in the real time implementations of large order linear and volterra filters for which both the ls and sg algorithms are unsuited

clebsch gordan coefficients for e6 and so 10 unification models we illustrate here a new method for computing clebsch gordan coefficients cgc for e6 by computing cgc for the product 27 27 of the irreducible representation 100000 of e6 with itself these cgc are calculated thrice once in a weight vector basis independent of any semisimple subgroup then in a basis which refers to so 10 e6 and finally in a basis referring to su 5 so 10 e6

a set of algorithms linking nlms and block rls algorithms this paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares nlms and the block recursive least squares brls algorithms all these algorithms use small block lengths thus allowing easy implementation and small input output delay it is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares lms algorithm while converging much faster a precise evaluation of the arithmetic complexity is provided and the adaptive behavior of the algorithm is analyzed simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the nlms algorithm the conclusions of the theoretical analysis are checked by simulations illustrating that even in the case where noise is added to the reference signal the proposed algorithm allows altogether a faster convergence and a lower residual error than the nlms algorithm finally a sample by sample version of this algorithm is outlined which is the link between the nlms and recursive least squares rls algorithms

cartan preserving automorphisms of untwisted and twisted kac moody algebras the group n defined as the normalizer of the cartan subalgebra in the group of all inner and outer automorphisms of affine kac moody km algebras is a natural extension of the weyl group and is shown to play a fundamental role in the structure of these algebras both untwisted and twisted it is a discrete galilean group which incorporates the affine and weyl group structure of the km algebra and the space time structure of the string it links the virasoro and km algebras in a nontrivial way and plays a key role in the vertex construction moreover the elements of its covering group can be used to uniquely parametrize and untwist the pseudotwisted km algebras

normalized lattice algorithms for least squares fir system identification recently developed algorithms for least squares identification of autoregressive models are extended in this paper so as to facilitate least squares identification of finite impulse response models the algorithms belong to the class of square root normalized lattice algorithms hence they share the computational efficiency and good numerical behavior of the latter two versions are presented one for identifying time invariant models and the other for tracking time varying parameters new lattice form realizations of the identified fir models are given the general framework is then specialized to the important cases of prediction and smoothing

computational improvement of the fast rm h _ infty filter based on information of input predictor a computationally reduced version of the fast hinfin filter fhf is derived under the assumption that the input signal to the unknown system can be represented by an autoregressive ar model whose order m is much lower than the filter length n the resulting filter referred to as the predictor based fast hinfin filter p fhf has a computational requirement of 3n o m multiplications per iteration which is considerably lower than the requirement for the fhf if is sufficiently smaller than n the validity of the p fhf are confirmed by computer simulations

stabilizing the fast kalman algorithms the fast kalman algorithms are stabilized by introducing a quantity that measures the accumulation of the roundoff errors this quantity is used to correct the variables of the algorithm at every time step the correction is defined as the solution of a specific minimization problem the resulting algorithm still has the nice complexity properties of the original algorithm linear in the number of parameters to be estimated but it has a much more stable behavior

branching rules for representations of simple lie algebras through weyl group orbit reduction two independent algorithms are presented which together allow the determination of branching rules from an irreducible representation of a compact lie algebra to those of a subalgebra or subjoined algebra the first gives the subalgebra weyl orbits contained in an algebra orbit the second gives the irreducible representations of an algebra contained in an orbit and by inversion of a triangular matrix the orbits contained in an irreducible representation