twisting and kappa poincare we demonstrate that the coproduct of and quantum poincare algebras in a classical algebra basis cannot be obtained by a cochain twist depending only on poincare algebra generators we also argue that the nonexistence of such a twist does not imply the nonexistence of a universal r matrix

representability and specht problem for g graded algebras abstract let w be an associative pi algebra over a field f of characteristic zero graded by a finite group g let id g w denote the t ideal of g graded identities of w we prove 1 g graded pi equivalence there exists a field extension k of f and a finite dimensional z 2 z g graded algebra a over k such that id g w id g a where a is the grassmann envelope of a 2 g graded specht problem the t ideal id g w is finitely generated as a t ideal 3 g graded pi equivalence for affine algebras let w be a g graded affine algebra over f then there exists a field extension k of f and a finite dimensional algebra a over k such that id g w id g a

identities and central polynomials with involution for the grassmann algebra abstract let e be the infinite dimensional grassmann algebra over an infinite field of characteristic p different from 2 given an involution on e denote by i d e and c e the set of all polynomial identities and central polynomials of e respectively in this paper we describe i d e and c e moreover we prove that c e is not finitely generated as a t space if p 2

graded identities of matrix algebras and the universal graded algebra in the last decade group gradings and graded identities of finite dimensional central simple algebras have been an active area of research we refer the reader to bahturin et al 6 and 7 there are two basic kinds of group grading elementary and fine it was proved by bahturin and zaicev 7 that any group grading of mn c is given by a certain composition of an elementary grading and a fine grading in this paper we are concerned with fine gradings on mn c and their corresponding graded identities let r be a simple algebra finite dimensional over its center k and g a finite group we say that r is fine graded by g if r g grg is a grading and dimk rg 1 thus any component is either 0 or isomorphic to k as a k vector space it is easy to show that supp r the subset of elements of g for which rg is not 0 is a subgroup of g moreover

an efficient robust adaptive filtering algorithm based on parallel subgradient projection techniques this paper presents a novel robust adaptive filtering scheme based on the interactive use of statistical noise information and the ideas developed originally for efficient algorithmic solutions to the convex feasibility problems the statistical noise information is quantitatively formulated as stochastic property closed convex sets by the simple design formulae developed in this paper a simple set theoretic inspection also leads to an important statistical reason for the sensitivity to noise of the affine projection algorithm apa the proposed adaptive algorithm is computationally efficient and robust to noise because it requires only an iterative parallel projection onto a series of closed half spaces that are highly expected to contain the unknown system to be identified and is free from the computational load of solving a system of linear equations the numerical examples show that the proposed adaptive filtering scheme realizes dramatically fast and stable convergence for highly colored excited speech like input signals in severe noise situations

a family of shrinkage adaptive filtering algorithms a family of adaptive filtering algorithms that uses a variable step size is proposed a variable step size is obtained by minimizing the energy of the noise free a posteriori error signal which is obtained by using a known l 1 hbox l 2 minimization formulation based on this methodology a shrinkage affine projection shap algorithm a shrinkage least mean squares shlms algorithm and a shrinkage normalized least mean squares shnlms algorithm are proposed the shap algorithm yields a significantly reduced steady state misalignment as compared to the conventional affine projection ap variable step size ap and set membership ap algorithms for the same convergence speed although the improvement is achieved at the cost of an increase in the average computational effort per iteration in the amount of 11 to 14 the shlms algorithm yields a significantly reduced steady state misalignment and faster convergence as compared to the conventional lms and variable step size lms algorithms similarly the shnlms algorithm yields a significantly reduced steady state misalignment and faster convergence as compared to the conventional normalized least mean squares nlms and set membership nlms algorithms

author s reply to comments on variable explicit regularization in affine projection algorithm robustness issues and optimal choice muralidhar et al point out that when the vr apa is applied in echo cancellation it will diverge during the presence of a near end signal or a silence period we provide an explanation for the behavior of the algorithm and show that a double talk detector makes the vr apa suitable for this application

star polynomial identities computing the exponential growth of the codimensions abstract can one compute the exponential rate of growth of the codimensions of a pi algebra with involution over a field of characteristic zero it was shown in 2 that any such algebra a has the same identities as the grassmann envelope of a finite dimensional superalgebra with superinvolution b here by exploiting this result we are able to provide an exact estimate of the exponential rate of growth e x p a of any pi algebra a with involution it turns out that e x p a is an integer and in case the base field is algebraically closed it coincides with the dimension of an admissible subalgebra of maximal dimension of b

de rham cohomology and hodge decomposition for quantum groups istvan heckenberger and axel schuler abstra t let z be one of the n dimensional bicovariant first order differential calculi for the quantum groups glq n slq n soq n or spq n where q is a transcendental complex number and z is a regular parameter it is shown that the de rham cohomology of woronowicz external algebra coincides with the de rham cohomologies of its left coinvariant its right coinvariant and its twosided coinvariant subcomplexes in the cases glq n and slq n the cohomology ring is isomorphic to the coinvariant external algebra inv and to the vector space of harmonic forms we prove a hodge decomposition theorem in these cases the main technical tool is the spectral decomposition of the quantum laplace beltrami operator

on the codimension sequence of g simple algebras abstract let f be an algebraically closed field of characteristic zero and let g be a finite group in this paper we will show that the asymptotics of c n g a the g graded codimension sequence of a finite dimensional g simple f algebra a has the form n 1 dim f a e 2 dim f a n as conjectured by e aljadeff d haile and m natapov where is some positive real number and a e denotes the identity component of a in the special case where a is the algebra of m m matrices with an arbitrary elementary g grading we succeeded in calculating the constant explicitly

variable explicit regularization in affine projection algorithm robustness issues and optimal choice a variable regularized affine projection algorithm vr apa is introduced without requiring the classical step size its use is supported from different points of view first it has the property of being hinfin optimal and it satisfies certain error energy bounds second the time varying regularization parameter is obtained by maximizing the speed of convergence of the algorithm although we first derive the vr apa for a linear time invariant lti system we show that the same expression holds if we consider a time varying system following a first order markov model we also find expressions for the power of the steady state error vector for the vr apa and the standard apa with no regularization parameter particularly we obtain quite different results with and without using the independence assumption between the a priori error vector and the measurement noise vector simulation results are presented to test the performance of the proposed algorithm and to compare it with other schemes under different situations an important conclusion is that the former independence assumption can lead to very inaccurate steady state results especially when high values of the projection order are used

comments on variable explicit regularization in affine projection algorithm robustness issues and optimal choice the above paper presented a variable regularized affine projection algorithm vr apa a delay coefficients based variable regularized affine algorithm dc vr apa was presented in 2 3 it was shown in 1 pp 2103 39 that dc vr apa is an equivalent and alternate manifestation of the vr apa when the affine projection order is equal to 1 however results pertaining to input speech signals and presence of near end speech activity 1 were not reported in for the same set of parameters this letter 2 shows that dc vr apa is more robust to the above conditions than the vr apa motivated by some of the explanations in we present the reasons for the robustness of dc vr apa in the above conditions

quantum poincare group related to the kappa poincare algebra the classical r matrix implied by the quantum kappa poincare algebra of lukierski nowicki and ruegg is used to generate a poisson structure on the poincare group a quantum deformation of the poincare group on the hopf algebra level is obtained by a trivial quantization

a time domain feedback analysis of filtered error adaptive gradient algorithms this paper provides a time domain feedback analysis of gradient based adaptive schemes a key emphasis is on the robustness performance of the adaptive filters in the presence of disturbances and modeling uncertainties along the lines of h sup spl infin theory and robust filtering the analysis is carried out in a purely deterministic framework and assumes no prior statistical information or independence conditions it is shown that an intrinsic feedback structure can be associated with the varied adaptive schemes the feedback structure is motivated via energy arguments and is shown to consist of two major blocks a time variant lossless i e energy preserving feedforward path and a time variant feedback path the configuration is further shown to lend itself to analysis via a so called small gain theorem thus leading to stability and robustness conditions that require the contractivity of certain operators choices for the step size parameter in order to guarantee faster rates of convergence are also derived and simulation results are included to demonstrate the theoretical findings in addition the time domain analysis provided in this paper is shown to extend the so called transfer function approach to a general time variant scenario without any approximations

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

convergence behavior of affine projection algorithms a class of equivalent algorithms that accelerate the convergence of the normalized lms nlms algorithm especially for colored inputs has previously been discovered independently the affine projection algorithm apa is the earliest and most popular algorithm in this class that inherits its name the usual apa algorithms update weight estimates on the basis of multiple unit delayed input signal vectors we analyze the convergence behavior of the generalized apa class of algorithms allowing for arbitrary delay between input vectors using a simple model for the input signal vectors conditions for convergence of the apa class are derived it is shown that the convergence rate is exponential and that it improves as the number of input signal vectors used for adaptation is increased however the rate of improvement in performance time to steady state diminishes as the number of input signal vectors increases for a given convergence rate apa algorithms are shown to exhibit less misadjustment steady state error than nlms simulation results are provided to corroborate the analytical results

quantum group gauge theory on quantum spaces we construct quantum group valued canonical connections on quantum homogeneous spaces including aq deformed dirac monopole on the quantum sphere of podles with quantum differential structure coming from the 3d calculus of woronowicz onsu q 2 the construction is presented within the setting of a general theory of quantum principal bundles with quantum group hopf algebra fibre associated quantum vector bundles and connection one forms both the base space spacetime and the total space are non commutative algebras quantum spaces

on twisting of finite dimensional hopf algebras in this paper we study the properties of drinfeld s twisting for finite dimensional hopf algebras we determine how the integral of the dual to a unimodular hopf algebra h changes under twisting of h we show that the classes of cosemisimple unimodular cosemisimple involutive cosemisimple quasitriangular finite dimensional hopf algebras are stable under twisting we also prove the cosemisimplicity of a coalgebra obtained by twisting of a cosemisimple unimodular hopf algebra by two different twists on two sides such twists are closely related to bi galois extensions and describe the representation theory of its dual next we define the notion of a non degenerate twist for a hopf algebra h and set up a bijection between such twists for h and h this bijection is based on miyashita ulbrich actions of hopf algebras on simple algebras it generalizes to the non commutative case the procedure of inverting a non degenerate skew symmetric bilinear form on a vector space finally we apply these results to classification of twists in group algebras and of cosemisimple triangular finite dimensional hopf algebras in positive characteristic generalizing the previously known classification in characteristic zero

pre torsors and equivalences abstract properties of most general non commutative torsors or a b torsors are analysed starting with pre torsors it is shown that they are equivalent to a certain class of galois extensions of algebras by corings it is shown that a class of faithfully flat pre torsors induces equivalences between categories of comodules of associated corings it is then proven that a b torsors correspond to monoidal functors and under some additional conditions equivalences between categories of comodules of bialgebroids

algebraic aspects of the quantum yang baxter equation in this paper we examine a variety of algebraic contexts in which the quantum yang baxter equation arises and derive methods for generating new solutions from given ones the solutions we describe are encoded in objects which have a module and a comodule structure over a bialgebra our work here is based in part on the ideas of dr1 dr2 suppose that r m m m m is a solution to the quantum yang baxter equation where m is a finite dimensional vector space over a field k in dr2 it was shown that r can be derived from a left h module structure and a right h comodule structure on m for some bialgebra h over k also see yet maj1 maj2 frt2 the module and comodule structure satisfy a natural compatibility condition m together with these structures is called a left quantum yang baxter h module every left quantum yang baxter module gives rise to a solution to the quantum yang baxter equation in a natural way we study the category hyb of left quantum yang baxter h modules and show that many of the familiar constructions in the module category hm can be made in hyb through these constructions solutions to the quantum yang baxter equation can be combined in various ways to generate new ones we place particular emphasis on the tensor product of objects of hyb and ways in which the tensor algebra t m of an object m of hyb can be viewed as an object of hyb using the tensor algebra we are able to extend certain solutions when dim m 2 to the quantum plane we turn the tensor algebra t m of an object m of hyb into an object of hyb by giving it a module algebra and a comodule algebra structure module algebra and comodule algebra structures play a very important role in this paper in section 9 we develop a calculus for uq sl2 starting with a right k slq 2 comodule algebra structure on the quantum plane k x y q where k slq 2 is the coordinate ring of quantum slq 2 over k this calculus has been described in other ways m s sud the right comodule algebra structure on k x y q accounts for the left uq sl2 module algebra structure on k x y q described in m s we show how the basic irreducible representations of tak follow by the calculus a module algebra action or comodule algebra action is a natural vehicle for extending structure on a submodule or subcomodule respectively to the subalgebra it generates the calculus and the solutions to the quantum yang baxter equation we describe in this paper are determined in this manner on small structures two dimensional in this case we believe that many more results will follow from this circle of ideas in section 2 we discuss basic aspects of coalgebra and bialgebras used in the sequel a good general reference for this is sweedler s book sb on hopf algebras in section 3 we review the quantum yang baxter equation in connection with quantum yang baxter modules the a r construction of faddeev reshetikhin and takhtajan frt is considered in this light and examined in detail in when r arises from two commuting operators even though this particular r is rather simple the algebra structure of a r is surprisingly complex using the scratchpad computer algebra system we determine the algebra structure of a r in an interesting specific case showing that our particular example has a finite non commutative groeb

h sup spl infin optimality of the lms algorithm we show that the celebrated least mean squares lms adaptive algorithm is h sup spl infin optimal the lms algorithm has been long regarded as an approximate solution to either a stochastic or a deterministic least squares problem and it essentially amounts to updating the weight vector estimates along the direction of the instantaneous gradient of a quadratic cost function we show that the lms can be regarded as the exact solution to a minimization problem in its own right namely we establish that it is a minimax filter it minimizes the maximum energy gain from the disturbances to the predicted errors whereas the closely related so called normalized lms algorithm minimizes the maximum energy gain from the disturbances to the filtered errors moreover since these algorithms are central h sup spl infin filters they minimize a certain exponential cost function and are thus also risk sensitive optimal we discuss the various implications of these results and show how they provide theoretical justification for the widely observed excellent robustness properties of the lms filter

linear estimation in krein spaces i theory the authors develop a self contained theory for linear estimation in krein spaces the derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between krein space projection and the recursive computation of the stationary points of certain second order or quadratic forms the authors use the innovations process to obtain a general recursive linear estimation algorithm when specialized to a state space structure the algorithm yields a krein space generalization of the celebrated kalman filter with applications in several areas such as h sup spl infin filtering and control game problems risk sensitive control and adaptive filtering

p i algebras with hopf algebra actions abstract ifais a p i algebra in characteristic zero with action from a finite dimensional semisimple hopf algebrah thenahas a nilpotenth idealnsuch thata nwill beh verbally semiprime everyh verbally semiprime algebra ish p i equivalent to a direct sum ofh verbally prime algebras in the case of a finite group action or a grading by an abelian group we show that the sum can be taken to be finite in the case of an action by a finite cyclic groupg we classify allg p i algebras up to equivalence this paper generalizes the work of a r kerner 1985 math ussr izv 25

strong connections on quantum principal bundles a gauge invariant notion of a strong connection is presented and characterized it is then used to justify the way in which a global curvature form is defined strong connections are interpreted as those that are induced from the base space of a quantum bundle examples of both strong and non strong connections are provided in particular such connections are constructed on a quantum deformation of the two sphere fibrations2 rp2 a certain class of stronguq 2 connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with theq dependent hermitian metric a particular form of the yang mills action on a trivialuq 2 bundle is investigated it is proved to coincide with the yang mills action constructed by a connes and m rieffel furthermore it is shown that the moduli space of critical points of this action functional is independent ofq

pseudo affine projection algorithms revisited robustness and stability analysis the so called affine projection ap algorithm is of large interest in many adaptive filters applications due to its considerable speed up in convergence compared to its simpler version the lms algorithm while the original ap algorithm is well understood gradient type variants of less complexity with relaxed step size conditions called pseudo affine projection offer still unresolved problems this contribution shows i local robustness properties of such algorithms ii global properties of these concluding l2 stability conditions that are independent of the input signal statistics as well as iii steady state values of moderate to high accuracy by relatively simple terms when applied to long filters of particular interest is the existence of lower step size bounds for one of the variants a bound that has not been observed before

graded polynomial identities and codimensions computing the exponential growth abstract let g be a finite abelian group and a a g graded algebra over a field of characteristic zero this paper is devoted to a quantitative study of the graded polynomial identities satisfied by a we study the asymptotic behavior of c n g a n 1 2 the sequence of graded codimensions of a and we prove that if a satisfies an ordinary polynomial identity lim n c n g a n exists and is an integer we give an explicit way of computing such integer by proving that it equals the dimension of a suitable finite dimension semisimple g z 2 graded algebra related to a

kemer s theory for h module algebras with application to the pi exponent abstract let h be a semisimple finite dimensional hopf algebra over a field f of zero characteristic we prove three major theorems 1 the representability theorem which states that every h module associative f algebra w satisfying an ordinary pi has the same h identities as the grassmann envelope of an h f z 2 z module algebra which is finite dimensional over a field extension of f 2 the specht problem for h module ordinary pi algebras that is every h t ideal which contains an ordinary pi contains h polynomials f 1 f s which generate as an h t ideal 3 amitsur s conjecture for h module algebras saying that the exponent of the h codimension sequence of an ordinary pi h module algebra is an integer

finitely generated algebras with involution and their identities abstract we consider associative algebras with involution over a field of characteristic zero in this case we prove that for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution which satisfies the same identities with involution this is an analogue and an extension of the theorem of a r kemer for ordinary identities kemer 1991 8 the similar results were proved earlier by the author for identities graded by a finite abelian group sviridova 2011 15 and by e aljadeff and a kanel belov 2010 1 for identities graded by any finite group

a column generation technique for the computation of stationary points in two recent papers eaves showed that lemke s algorithm can be used to compute a stationary point of an affine function over a polyhedral set this paper proposes an alternative method which is based on parametric principal pivoting the proposed method involves solving systems of linear equations and parametric linear subprograms over the given polyhedral set an obvious advantage of the method is that any special structure of the polyhedral set can be exploited profitably in the solution of the subprograms

weyl wigner formulation of noncommutative quantum mechanics we address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension displaying both spatial and momentum noncommutativities by resorting to a covariant generalization of the weyl wigner transform and to the darboux map we construct an isomorphism between the operator and the phase space representations of the extended heisenberg algebra this map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space we construct the extended star product and moyal bracket and propose a general definition of noncommutative states we study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of the darboux map our approach unifies and generalizes all the previous proposals for the phase space formulation of noncommutative quantum mechanics for concreteness we rederive these proposals by restricting our formalism to some two dimensional spaces

a characterization of minimal varieties of zp graded pi algebras abstract let f be a field of characteristic zero and p a prime in the present paper it is proved that a variety of z p graded associative pi f algebras of finite basic rank is minimal of fixed z p exponent d if and only if it is generated by an upper block triangular matrix algebra u t z p a 1 a m equipped with a suitable elementary z p grading whose diagonal blocks are isomorphic to z p graded simple algebras a 1 a m satisfying dim f a 1 a m d

verbally prime t ideals and graded division algebras abstract let f be an algebraically closed field of characteristic zero and let g be a finite group we consider graded verbally prime t ideals in the free g graded algebra it turns out that equivalent definitions in the ordinary case i e ungraded extend to nonequivalent definitions in the graded case namely verbally prime g graded t ideals and strongly verbally prime t ideals at first following kemer s ideas we classify g graded verbally prime t ideals the main bulk of the paper is devoted to the stronger notion we classify g graded strongly verbally prime t ideals which are t ideal of affine g graded algebras or equivalently g graded t ideals that contain a capelli polynomial it turns out that these are precisely the t ideal of g graded identities of finite dimensional g graded central over f i e z a e f which admit a g graded division algebra twisted form over a field k which contains f or equivalently over a field k which contains enough roots of unity e g a primitive n root of unity where n o r d g

from supersymmetry to quantum commutativity abstract let h r be a quasitriangular hopf algebra acting on an algebra a we study a concept of a being quantum commutative with respect to h r superalgebras which are graded commutative called sometimes commutative superalgebras are shown to be examples of such an action there is an analogous notion of quantum commutativity for comodule algebra the quantum plane cq x y is an example both under the coaction of quantum 2 2 matrices and also in a more novel way at q a root of unity if h is a cocommutative finite dimensional hopf algebra and d h r its drinfeld double we show that h is quantum commutative with respect to d h r we discuss further examples of such actions and coactions and show that the category a hmod resembles for such actions the category of modules over commutative rings

group graded algebras and almost polynomial growth let f be a field of characteristic 0 g a finite abelian group and a a g graded algebra we prove that a generates a variety of g graded algebras of almost polynomial growth if and only if a has the same graded identities as one of the following algebras 1 fcp the group algebra of a cyclic group of order p where p is a prime number and p g 2 ut2g f the algebra of 2 2 upper triangular matrices over f endowed with an elementary g grading 3 e the infinite dimensional grassmann algebra with trivial g grading 4 in case 2 g ez2 the grassmann algebra with canonical z2 grading

remarks on simple interpolation between jordanian twists in this paper we propose a simple generalization of the locally r symmetric jordanian twist resulting in the one parameter family of jordanian twists all the proposed twists differ by the coboundary twists and produce the same jordanian deformation of the corresponding lie algebra they all provide the minkowski spacetime commutation relations constructions from noncommutative coordinates to the star product and coproduct and from the star product to the coproduct and the twist are presented the corresponding twist in the hopf algebroid approach is given our results are presented symbolically by a diagram relating all of the possible constructions

noncommutative riemannian and spin geometry of the standard q sphere we study the quantum sphere open image in new window as a quantum riemannian manifold in the quantum frame bundle approach we exhibit its 2 dimensional cotangent bundle as a direct sum 0 1 1 0 in a double complex we find the natural metric volume form hodge operator laplace and maxwell operators and projective module structure we show that the q monopole as spin connection induces a natural levi civita type connection and find its ricci curvature and q dirac operator open image in new window we find the possibility of an antisymmetric volume form quantum correction to the ricci curvature and lichnerowicz type formulae for open image in new window we also remark on the geometric q borel weil bott construction

mean square performance of a family of affine projection algorithms affine projection algorithms are useful adaptive filters whose main purpose is to speed the convergence of lms type filters most analytical results on affine projection algorithms assume special regression models or gaussian regression data the available analysis also treat different affine projection filters separately this paper provides a unified treatment of the mean square error tracking and transient performances of a family of affine projection algorithms the treatment relies on energy conservation arguments and does not restrict the regressors to specific models or to a gaussian distribution simulation results illustrate the analysis and the derived performance expressions

an equivalence between two algorithms for quadratic programming in this paper we demonstrate that the van de panne whinston symmetric simplex method when applied to a certain implicit formulation of a quadratic program generates the same sequence of primal feasible vectors as does the von hohenbalken simplicial decomposition algorithm specialized to the same program such an equivalence of the two algorithms extends earlier results for a least distance program due to cottle djang

wigner functions on non standard symplectic vector spaces we consider the weyl quantization on a flat non standard symplectic vector space we focus mainly on the properties of the wigner functions defined therein in particular we show that the sets of wigner functions on distinct symplectic spaces are different but have non empty intersections this extends previous results to arbitrary dimension and arbitrary constant symplectic structure as a by product we introduce and prove several concepts and results on non standard symplectic spaces which generalize those on the standard symplectic space namely the symplectic spectrum williamson s theorem and narcowich wigner spectra we also show how wigner functions on non standard symplectic spaces behave under the action of an arbitrary linear coordinate transformation

on z2 graded identities of ut2 e and their growth abstract let f be an infinite field of characteristic different from two and e be the infinite dimensional grassmann algebra over f we consider the upper triangular matrix algebra ut 2 e with entries in e endowed with the z 2 grading inherited by the natural z 2 grading of e and we study its ideal of z 2 graded polynomial identities t z 2 ideal and its relatively free algebra in particular we show that the set of z 2 graded polynomial identities of ut 2 e does not depend on the characteristic of the field moreover we compute the z 2 graded hilbert series of ut 2 e and its z 2 graded gelfand kirillov dimension

generalized diagonal crossed products and smash products for quasi hopf algebras applications in this paper we introduce generalizations of diagonal crossed products two sided crossed products and two sided smash products for a quasi hopf algebra h the results we obtain may then be applied to h hopf bimodules and generalized yetter drinfeld modules the generality of our situation entails that the generating matrix formalism cannot be used forcing us to use a different approach this pays off because as an application we obtain an easy conceptual proof of an important but very technical result of hausser and nill concerning iterated two sided crossed products

equivalence of some quadratic programming algorithms we formulate a general algorithm for the solution of a convex but not strictly convex quadratic programming problem conditions are given under which the iterates of the algorithm are uniquely determined the quadratic programming algorithms of fletcher gill and murray best and ritter and van de panne and whinston dantzig are shown to be special cases and consequently are equivalent in the sense that they construct identical sequences of points the various methods are shown to differ only in the manner in which they solve the linear equations expressing the kuhn tucker system for the associated equality constrained subproblems equivalence results have been established by goldfarb and djang for the positive definite hessian case our analysis extends these results to the positive semi definite case

graded polynomial identities of matrices we consider g graded polynomial identities of the p p matrix algebra mp k over a field k of characteristic 0 graded by an arbitrary group g we find relations between the g graded identities of the g graded algebra mp k and the g h graded identities of the tensor product of mp k and the h graded algebra mq k with a fine h grading we also find a basis of the g graded identities of mp k with an elementary grading such that the identity component coincides with the diagonal of mp k

noncommutative principal bundles through twist deformation we construct noncommutative principal bundles deforming principal bundles with a drinfeld twist 2 cocycle if the twist is associated with the structure group then we have a deformation of the fibers if the twist is associated with the automorphism group of the principal bundle then we obtain noncommutative deformations of the base space as well combining the two twist deformations we obtain noncommutative principal bundles with both noncommutative fibers and base space more in general the natural isomorphisms proving the equivalence of a closed monoidal category of modules and its twist related one are used to obtain new hopf galois extensions as twists of hopf galois extensions a sheaf approach is also considered and examples presented

bialgebroids a bialgebras and duality an equivalence between lu s bialgebroids xu s bialgebroids with an anchor and takeuchi s a bialgebras is explicitly proven a new class of examples of bialgebroids is constructed a formal dual of a bialgebroid termed bicoalgebroid is defined a weak hopf algebra is shown to be an example of such a bicoalgebroid

graded identities of block triangular matrices abstract let f be an infinite field and u t d 1 d n be the algebra of upper block triangular matrices over f in this paper we describe a basis for the g graded polynomial identities of u t d 1 d n with an elementary grading induced by an n tuple of elements of a group g such that the neutral component corresponds to the diagonal of u t d 1 d n in particular we prove that the monomial identities of such algebra follow from the ones of degree up to 2 n 1 our results generalize for infinite fields of arbitrary characteristic previous results in the literature which were obtained for fields of characteristic zero and for particular g gradings in the characteristic zero case we also generalize results for the algebra u t d 1 d n c with a tensor product grading where c is a color commutative algebra generating the variety of all color commutative algebras

specht property for some varieties of jordan algebras of almost polynomial growth abstract let f be a field of characteristic zero in 25 it was proved that u j 2 the jordan algebra of 2 2 upper triangular matrices can be endowed up to isomorphism with either the trivial grading or three distinct non trivial z 2 gradings or by a z 2 z 2 grading in this paper we prove that the variety of jordan algebras generated by u j 2 endowed with any g grading has the specht property i e every t g ideal containing the graded identities of u j 2 is finitely based moreover we prove an analogue result about the ordinary identities of a 1 a suitable infinitely generated metabelian jordan algebra defined in 27

on group gradings on pi algebras abstract we show that there exists a constant k such that for any pi algebra w and any nondegenerate g grading on w where g is any group possibly infinite there exists an abelian subgroup u of g with g u exp w k a g grading w g g w g is said to be nondegenerate if w g 1 w g 2 w g r 0 for any r 1 and any r tuple g 1 g 2 g r in g r

normalized data nonlinearities for lms adaptation properly designed nonlinearly modified lms algorithms in which various quantities in the stochastic gradient estimate are operated upon by memoryless nonlinearities have been shown to perform better than the lms algorithm in system identification type problems the authors investigate one such algorithm given by w sub k l w sub k spl mu d sub k w sub k sup t x sub k x sub k f x sub k in which the function f x sub k is a scalar function of the sum of the squares of the n elements of the input data vector x sub k this form of algorithm generalizes the so called normalized lms nlms algorithm they evaluate the expected behavior of this nonlinear algorithm for both independent input vectors and correlated gaussian input vectors assuming the system identification model by comparing the nonlinear algorithm s behavior with that of the lms algorithm they then provide a method of optimizing the form of the nonlinearity for the given input statistics in the independent input case they show that the optimum nonlinearity is a single parameter version of the nlms algorithm with an additional constant in the denominator and show that this algorithm achieves a lower excess mean square error mse than the lms algorithm with an equivalent convergence rate additionally they examine the optimum step size sequence for the optimum nonlinear algorithm and show that the resulting algorithm performs better and is less complex to implement than the optimum step size algorithm derived for another form of the nlms algorithm simulations verify the theory and the predicted performance improvements of the optimum normalized data nonlinearity algorithm

mean square deviation analysis of affine projection algorithm this paper presents an improved mean square deviation msd analysis of the standard affine projection algorithm apa based on two distinctive features first the propagation model of the error covariance includes the cross correlation between the current weight error vector and the prior measurement noises associated with the reused inputs such a cross correlation has merely been considered previously second the analysis based on n most recent accumulated iterations rather than a typical analysis based on a current single iteration is suggested to reveal a previously unseen phenomenon where n denotes the tap length of the filter simulation results are in better agreement with the proposed theoretical results than the previous theoretical ones over a wide range of parameters such as tap length projection order and step size

the serre spectral sequence of a noncommutative fibration for de rham cohomology for differential calculi on noncommutative algebras we construct a twisted de rham cohomology using flat connections on modules this has propertie s similar in some respects to sheaf cohomology on topological spaces we also discuss generalised mapping properties of these theories and relations of these properties to corings using t his we give conditions for the serre spectral sequence to hold for a noncommutative fibration th is might be better read as giving the definition of a fibration in noncommutative differential geo metry we also study the multiplicative structure of such spectral sequences finally we show that some noncommutative homogeneous spaces satisfy the conditions to be such a fibration and in th e process clarify the differential structure on these homogeneous spaces we also give two explicit examples of differential fibrations these are built on the quantum hopf fibration with two differe nt differential structures

polynomial identities and noncommutative versal torsors abstract to any cleft hopf galois object i e any algebra h obtained from a hopf algebra h by twisting its multiplication with a two cocycle we attach two universal algebras a h and u h the algebra a h is obtained by twisting the multiplication of h with the most general two cocycle formally cohomologous to the cocycle takes values in the field of rational functions on h by construction a h is a cleft h galois extension of a big commutative algebra b h any form of h can be obtained from a h by a specialization of b h and vice versa if the algebra h is simple then a h is an azumaya algebra with center b h the algebra u h is constructed using a general theory of polynomial identities that we set up for arbitrary comodule algebras it is the universal comodule algebra in which all comodule algebra identities of h are satisfied we construct an embedding of u h into a h this embedding maps the center z h of u h into b h when the algebra h is simple in this case under an additional assumption a h b h z h u h thus turning a h into a central localization of u h we completely work out these constructions in the case of the four dimensional sweedler algebra