corrected confidence bands for functional data using principal components functional principal components fpc analysis is widely used to decompose and express functional observations curve estimates implicitly condition on basis functions and other quantities derived from fpc decompositions however these objects are unknown in practice in this article we propose a method for obtaining correct curve estimates by accounting for uncertainty in fpc decompositions additionally pointwise and simultaneous confidence intervals that account for both model and decomposition based variability are constructed standard mixed model representations of functional expansions are used to construct curve estimates and variances conditional on a specific decomposition iterated expectation and variance formulas combine model based conditional estimates across the distribution of decompositions a bootstrap procedure is implemented to understand the uncertainty in principal component decomposition quantities our method compares favorably to competing approaches in simulation studies that include both densely and sparsely observed functions we apply our method to sparse observations of cd4 cell counts and to dense white matter tract profiles code for the analyses and simulations is publicly available and our method is implemented in the r package refund on cran

on the graded identities and cocharacters of the algebra of 3 3 matrices abstract let m2 1 f be the algebra of 3 3 matrices over an algebraically closed field f of characteristic zero with non trivial z 2 grading we study the graded identities of this algebra through the representation theory of the hyperoctahedral group z 2 s n after splitting the space of multilinear polynomial identities into the sum of irreducibles under the z 2 s n action we determine all the irreducible z 2 s n characters appearing in this decomposition with non zero multiplicity we then apply this result in order to study the graded cocharacter of the grassmann envelope of m2 1 f finally using the representation theory of the general linear group we determine all the graded polynomial identities of the algebra m2 1 f up to degree 5

on the structure of h sup infinity control systems and related extensions an existence condition of a h sup infinity controller which achieves a prescribed norm bound of the closed loop transfer function is derived in the frequency domain based on a generalization of the notion of j lossless systems this condition is regarded as a frequency domain representation of the well known existence condition in the state space represented in terms of the two algebraic riccati equations a notion of j orthogonal complement which is introduced as a generalization of the usual orthogonal complement play an important role in clarifying the fundamental frequency domain structure of the model matching problem and simplifying the computation of controllers the results are extended to the nonstandard case where the direct feedthrough from the input to the error or from the exogenous signal to the output is no longer of full rank it is shown that the proper controller achieving the prescribed norm bound exists even in this case in nonstandard cases the controller order can be smaller than the plant order

exponential codimension growth of pi algebras an exact estimate abstract letabe an associative pi algebra over a fieldfof characteristic zero by studying the exponential behavior of the sequence of codimensions cn a ofa we prove thatinv a limn c n a always exists and is an integer we also give an explicit way for computing such integer letbbe a finite dimensionalz2 graded algebra whose grassmann envelopeg b satisfies the same identities ofa theninv a inv g b dim c 0 dim c 1 wherec 0 c 1 is a suitablez2 graded semisimple subalgebra ofb

on some minimal supervarieties of exponential growth abstract in the present paper we investigate minimal supervarieties of given superexponent over fields of characteristic zero we show that any minimal supervariety of finite basic rank is generated by one of the minimal superalgebras introduced by giambruno and zaicev in 2003 furthermore it is proved that any minimal superalgebra whose graded simple components of the semisimple part are simple generates a minimal supervariety finally we state that the same conclusion holds when the semisimple part of a minimal superalgebra has exactly two arbitrary graded simple components

group gradings on associative algebras abstract let r g g rg be a g graded ring we describe all types of gradings on r if g is torsion free and r is artinian semisimple if r is a matrix algebra over an algebraically closed field f then we give a description of all g gradings on r provided that g is an abelian group in the case of an abelian group g we also classify all finite dimensional graded simple algebras and finite dimensional graded division algebras over an algebraically closed field of characteristic zero

minimal superalgebras generating minimal supervarieties it has been shown that in characteristic zero the generators of the minimal supervarieties of finite basic rank belong to the class of minimal superalgebras introduced by giambruno and zaicev trans am math soc 355 5091 5117 2003 in the present paper the complete list of minimal supervarieties generated by minimal superalgebras whose maximal semisimple homogeneous subalgebra is the sum of three graded simple algebras is provided as a consequence we negatively answer the question of whether any minimal superalgebra generates a minimal supervariety

structure of zariski closed algebras the objective of this paper is to describe the structure of zariski closed algebras which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields our results include a version of wedderburn s principal theorem as well as a more explicit description using representations in terms of gluing in wedderburn components finally we construct generic zariski closed algebras whose description is considerably more complicated than the description of generic algebra of finite dimensional algebras special attention is given to infinite dimensional algebras over finite fields

codimension growth and minimal superalgebras a celebrated theorem of kemer 1978 states that any algebra satisfying a polynomial identity over a field of characteristic zero is pi equivalent to the grassmann envelope g a of a finite dimensional superalgebra a in this paper by exploiting the basic properties of the exponent of a pi algebra proved by giambruno and zaicev 1999 we define and classify the minimal superalgebras of a given exponent over a field of characteristic zero in particular we prove that these algebras can be realized as block triangular matrix algebras over the base field the importance of such algebras is readily proved a is a minimal superalgebra if and only if the ideal of identities of g a is a product of verbally prime t ideals also such superalgebras allow us to classify all minimal varieties of a given exponent i e varieties v such that exp v d 2 and exp u d for all proper subvarieties u of v this proves in the positive a conjecture of drensky 1988 as a corollary we obtain that there is only a finite number of minimal varieties for any given exponent a classification of minimal varieties of finite basic rank was proved by the authors 2003 as an application we give an effective way for computing the exponent of a t ideal given by generators and we discuss the problem of what functions can appear as growth functions of varieties of algebras

content corrected tolerance limits based on the bootstrap this article considers k factor tolerance limits in which the p content is data dependent the proposed content corrected method is based on a bootstrap estimate of the given content and is shown to be robust in the sense of preserving the confidence coefficient for a variety of distributions for small or moderate sample sizes to all large samples we develop the theoretical basis for the asymptotic results and prove both asymptotic normality and weak consistency of the corresponding bootstrap statistic the method is shown to be asymptotically accurate with respect to the confidence coefficient for a wide class of distributions several simulations and two examples show the advantage of this method when the normality of the data cannot be assumed

singular j j lossless factorization for strictly proper functions singular j j lossless factorization for strictly proper functions is studied the method of infinite zero compensation derived by copeland and safonov is used to extend the results of kimura to singular systems since j j lossless factorization contains both inner outer factorization and wiener hopf spectral factorization as special cases the results obtained here unify previous results on singular factorization problems

inner outer factorization for strictly proper functions with j w axis zeros abstract this paper discussed the inner outer factorization for square real rational matrices which may have zeros on the j axis including infinity a factorization method is given in terms of the descriptor form representation of the rational matrix this method uses the solution of a generalized riccati equation we also propose an efficient computation algorithm for solving the generalized riccati equation

a simple state space design of an interactor for a non square system via system matrix pencil approach abstract the construction of an interactor cancelling the infinite zeros of a non square proper transfer matrix is discussed in this paper along the line of approach of b r copeland m g safonov int j robust nonlinear control 2 1992 139 in this paper some new properties of the infinite eigenstructure of the system matrix pencil of the transfer matrix are presented a simple state space design of the interactor is proposed by using these properties then some new features about state space relations among the original system the interactor and the compensated system are presented also several conditions about the invariance of the stabilizability or controllability between the state space realizations of the original system and the compensated system are shown furthermore the proposed method of designing the interactor in this paper can be applied to a tall or fat transfer matrix with full normal rank

exponential growth for codimensions of some p i algebras abstract by the giambruno zaicev theorem for associative p i algebras the exponential rate of growth of the codimensions of such a p i algebra is always a positive integer here we calculate that integer for various generic p i algebras which are given by a single identity these include capelli type identities and the various powers of the standard polynomials

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

the extended j spectral factorization for descriptor systems in this paper we study an extended j spectral factorization problem i e j spectral factorization problem for descriptor systems which may not have full column normal rank and may exhibit poles and zeros on the extended imaginary axis we present necessary and sufficient solvability conditions and develop a numerically reliable method for the underlying problem our method is implemented by using only orthogonal transformations and has an acceptable computational complexity

proper identities lie identities and exponential codimension growth abstract the exponent exp a of a pi algebra a in characteristic zero is an integer and measures the exponential rate of growth of the sequence of codimensions of a a giambruno m zaicev on codimension growth of finitely generated associative algebras adv math 140 1998 145 155 a giambruno m zaicev exponential codimension growth of p i algebras an exact estimate adv math 142 1999 221 243 in this paper we study the exponential rate of growth of the sequences of proper codimensions and lie codimensions of an associative pi algebra we prove that the corresponding proper exponent exists for all pi algebras except for some algebras of exponent two strictly related to the grassmann algebra we also prove that the lie exponent exists for any finitely generated pi algebra the value of both exponents is always equal to exp a or exp a 1

graded embeddings of finite dimensional simple graded algebras abstract let a b be finite dimensional g graded algebras over an algebraically closed field k with char k 0 where g is an abelian group and let id g a be the set of graded identities of a resp id g b we show that if a b are g simple then there is a graded embedding a b if and only if id g b id g a we also give a weaker generalization for the case where a is g semisimple and b is arbitrary

identities and isomorphisms of graded simple algebras abstract let g be an arbitrary abelian group and let a and b be two finite dimensional g graded simple algebras over an algebraically closed field f such that the orders of all finite subgroups of g are invertible in f we prove that a and b are isomorphic if and only if they satisfy the same g graded identities we also describe all isomorphism classes of finite dimensional g graded simple algebras

young derived sequences of sn characters abstract given the sequence n is an s n character n 0 we construct the young derived sequence y y n n 0 y n n j 0 j o n j cocharacters of p i algebras are always young derived v drensky j algebra 91 1984 1 17 we study the relations between and y and between deg n and deg y n when is supported on a strip their asymptotics as n lead to some interesting integration formulas

standard polynomials are characterized by their degree and exponent abstract by the giambruno zaicev theorem giambruno and zaicev 1999 5 the exponent exp a of a p i algebra a exists and is always an integer in berele and regev 2001 2 it was shown that the exponent exp st n of the standard polynomial st n of degree n is not smaller than the exponent of any polynomial of degree n here it is proved that exp st n is strictly larger than the exponent of any other polynomial of degree n which is not a multiple of st n

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

j factorizations of a general discrete time system abstract the problems of extending the j lossless conjugation the j j spectral factorization and the j j lossless factorization to a completely general discrete time system are considered existence conditions together with a numerically sound prototype algorithm for computing the factors are provided for a system having any type of singularity including arbitrary normal rank poles and zeros at infinity at zero or on the unit circle

tolerance bands for functional data often the object of inference in biomedical applications is a range that brackets a given fraction of individual observations in a population a classical estimate of this range for univariate measurements is a tolerance interval this article develops its natural extension for functional measurements a tolerance band and proposes a methodology for constructing its pointwise and simultaneous versions that incorporates both sparse and dense functional data assuming that the measurements are observed with noise the methodology uses functional principal component analysis in a mixed model framework to represent the measurements and employs bootstrapping to approximate the tolerance factors needed for the bands the proposed bands also account for uncertainty in the principal components decomposition simulations show that the methodology has generally acceptable performance unless the data are quite sparse and unbalanced in which case the bands may be somewhat liberal the methodology is illustrated using two real datasets a sparse dataset involving cd4 cell counts and a dense dataset involving core body temperatures

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

pi algebras and their cocharacters abstract all pi algebras r satisfy identities of the form f x y x 1 y 1 x 2 y 2 y n 1 x n theorem a the existence of these identities imply also that cocharacters x n r lie in a hook shaped strip of width depending on the degree of the minimal identity of r theorem c this extends a characterization of rings satisfying a capelli identity theorem b

a numerical design of interactors for general descriptor systems in this technical note we develop a numerically reliable method to design an interactor for a general descriptor system relative to a stability region cg and an offending zero set our main result is based on a condensed form this condensed form is independent of the offending zeros and is computed using only orthogonal transformations and hence is numerically backward stable

nonparametric regression analysis of longitudinal data abstract nonparametric methods are developed for estimating the dose effect when a response consists of correlated observations over time measured in a dose response experiment the methods can also be applied to data collected from a completely randomized design experiment methods are developed for the detection and description of the effects of dose time and their interaction the methods allow for individual variation in the timing and number of observations a generalization allowing baseline covariates to be incorporated is addressed these results may be used in an exploratory fashion in the process of building a random effects model for longitudinal data

distinguishability and agreement with continuous data the analysis of concordance among repeated measures has received a huge amount of attention in the statistical literature leading to a range of different approaches however because all the approaches are able to assess the closeness among the readings taken on the same subject the conclusions about the degree of concordance should be similar regardless the approach applied here two indices to assess the concordance among continuous repeated measures the intraclass correlation coefficient and the total deviation index are applied and compared in two case examples the first example concerns the repeatability of individual nutrient allocation strategy assessed by stable isotope analysis the second example dealt with the assessment of the concordance of functional magnetic resonance imaging data that shows spatial correlation the results differ depending upon the approach applied leading to contradictory conclusions about the degree of concordance the reason behind these results is discussed reaching the conclusion that the total deviation index is just assessing agreement among repeated measurements whereas the intraclass correlation coefficient assesses the concept of distinguishability among subjects that involves agreement among repeated measurements and spread of subjects at once therefore the best way to select the right approach is to understand the right question behind the research hypothesis copyright 2013 john wiley sons ltd

on the minimality of algebras with involution abstract in di vincenzo and la scala 2007 1 given a n tuple a 1 a n of finite dimensional simple algebras over a field of characteristic zero a block triangular matrix algebra with involution denoted by r ut a 1 a n was introduced and it was proved that any finite dimensional algebra with involution which is minimal with respect to its exponent is pi equivalent to r for a suitable choice of the algebras a i motivated by a conjecture stated in the same paper here we show that r is minimal when either it is symmetric or n 2

tolerance intervals for assessing individual bioequivalence evaluation of equivalence of two formulations of a drug typically entails the comparison of average bioavailabilities recently however authors have become aware that this may be insufficient to assess individual bioequivalence that is interchangeability of formulations on an individual basis this paper outlines a tolerance interval procedure to assess individual bioequivalence based on a model that includes a subject by formulation interaction we give methods for several higher order cross over designs along with examples

graded identities and isomorphisms on algebras of upper block triangular matrices abstract let g be an abelian group and k an algebraically closed field of characteristic zero a valenti and m zaicev described the g gradings on upper block triangular matrix algebras provided that g is finite we prove that their result holds for any abelian group g any grading is isomorphic to the tensor product a b of an elementary grading a on an upper block triangular matrix algebra and a division grading b on a matrix algebra we then consider the question of whether graded identities a b where b is an algebra with a division grading determine a b up to graded isomorphism in our main result theorem 3 we reduce this question to the case of elementary gradings on upper block triangular matrix algebras which was previously studied by o m di vincenzo and e spinelli

lie solvability and the identity x1 y1 x2 y2 xq yq 0 in certain matrix algebras abstract we study the interplay between the polynomial identities x 1 x 2 x 3 x q 1 0 x 1 y 1 x 2 y 2 x q y q 0 and x 1 y 1 x 2 y 2 0 in general and in certain matrix algebras which are closely related to structural matrix algebras in particular we show that if such a matrix algebra a satisfies the identity x 1 y 1 x 2 y 2 0 in particular if a satisfies the identity x 1 x 2 x 3 0 then a satisfies the identity x 1 y 1 x 2 y 2 0 and we prove a decomposition theorem for such subalgebras of upper triangular matrix algebras satisfying the engel condition and hence for such lie nilpotent subalgebras an in depth analysis of the maximum dimension of a subalgebra of the full n n matrix algebra m n f over a field f satisfying the identity x 1 y 1 x 2 y 2 x q y q 0 as obtained in 5 leads to a more detailed formula for this maximum dimension as well to a precise way of obtaining a class of examples of f subalgebras of m n f having this dimension and finally to determining exactly when a simplified version of the mentioned formula can be used

minimal varieties of algebras of exponential growth abstract the exponent of a variety of algebras over a field of characteristic zero has been recently proved to be an integer through this scale we can now classify all minimal varieties of given exponent and of finite basic rank as a consequence we describe the corresponding t ideals of the free algebra and we compute the asymptotics of the related codimension sequences verifying in this setting some known conjectures we also show that the number of these minimal varieties is finite for any given exponent we finally point out some relations between the exponent of a variety and the gelfand kirillov dimension of the corresponding relatively free algebras of finite rank

jordan α β derivations on triangular algebras and related mappings abstract let r be a 2 torsion free commutative ring with identity a b be unital algebras over r and m be a unital a b bimodule which is faithful as a left a module and also as a right b module let t a m 0 b be the triangular algebra consisting of a b and m and let d be an r linear mapping from t into itself suppose that a and b have only trivial idempotents then the following statements are equivalent 1 d is a jordan derivation on t 2 d is a jordan triple derivation on t 3 d is an derivation on t furthermore a generalized version of this result is also given we characterize the actions of automorphisms and skew derivations on the triangular algebra t the structure of continuous derivations of triangular banach algebras and that of generalized jordan derivations of upper triangular matrix algebras are described

graded polynomial identities on upper block triangular matrix algebras let g be an arbitrary abelian group in the present paper we study the question of whether g graded upper block triangular matrix algebras over a field of characteristic zero are determined up to g graded isomorphism by their g graded polynomial identities we obtain some results for an elementary grading and as a consequence for any grading over an algebraically closed field

on extended j j lossless factorization abstract the extended j j lossless factorization for discrete time rational matrix functions with zeros on the unit circle is considered a necessary and sufficient condition for the existence of the extended j j lossless factorization is obtained the condition is given in terms of the original system parameters in the form of a generalized eigenvalue problem and a discrete time algebraic riccati equation state space representations for the extended j j lossless factorization are provided

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

computation of the general j j prime lossless factorization the j j lossless factorization problem for a generalized state space system whose transfer matrix is completely general is investigated the main novelty is that we remove all restrictive hypotheses and allow for arbitrary normal rank poles and zeros on the imaginary axis or at infinity the numerically sound formulas for the solution bear the same nice expressions and striking simplicity of the inner outer factorization and may be equally well applied for the j j spectral factorization

h control problem with jω axis zeros abstract in this paper we discuss the so called one block h control problem in the case where the plant has j axis including infinity poles and zeros first we derive a necessary and sufficient condition for the h model matching problem to have a solution in the transfer function setting second we give a solvability condition which enables us to check the solvability by i examining matrix norm conditions related to j axis zeros and ii solving two generalized riccati equations finally we extend our result to the standard h problem

sensitivity minimization in an h norm parametrization of all suboptimal solutions a number of problems in the control of linear feedback systems can be reduced to the following we are given three stable rational matrix functions k of sizes p 1 x q 1 p 1 x q 2 and p 2 x q 1 respectively and seek a stable rational q 2 x p 2 matrix function s so as to minimize k s we assume that p 1 q 2 p 2 q 1 and that and have maximal rank q 2 and p 2 respectively on the j axis given a tolerance level sufficiently large we obtain a linear fractional map g f 0 11 g 0 12 0 13 0 21 g 0 22 0 23 1 such that f k s with s stable and f if and only if g is a stable q 2 x p 2 matrix function with g 1 the computation of 0 0 ij 1 i 2 1 j 3 reduces to solving a pair of symmetric wiener hopf factorization problems for the special case where i q2 0 t i p2 0 and k not necessarily stable to which the general case can be reduced we provide explicit state space formulae for 0 in terms of a state space realization of k and the

block triangular matrix algebras and factorable ideals of graded polynomial identities abstract we study the graded polynomial identities of block triangular matrix algebras with respect to the grading defined by an abelian group g in particular we describe conditions for the t g ideal of a such algebra to be factorable as a product of t g ideals corresponding to the algebras defining the diagonal blocks moreover for the factorable t 2 ideal of a superalgebra we give a formula for computing its sequence of graded cocharacters once given the sequences of cocharacters of the t 2 ideals that factorize it we finally apply these results to a specific example of block triangular matrix superalgebra

principal modes of variation for processes with continuous sample curves analysis of a process with continuous sample curves can be carried out in a manner similar to principal components analysis of vector processes by appropriate definition of a best linear model in the continuous case we show that principal modes of variation consist of eigenfunctions of the process covariance function c s t procedures for estimation of these eigenfunctions from a finite sample of observed curves are given and results are compared with principal components analysis of the same data

gradings on the algebra of upper triangular matrices and their graded identities abstract let k be an infinite field and let ut n k denote the algebra of n n upper triangular matrices over k we describe all elementary gradings on this algebra further we describe the generators of the ideals of graded polynomial identities of ut n k and we produce linear bases of the corresponding relatively free graded algebras we prove that one can distinguish the elementary gradings by their graded identities we describe bases of the graded polynomial identities in several typical cases although in these cases we consider elementary gradings by cyclic groups the same methods serve for elementary gradings by any finite group

on codimension growth of finitely generated associative algebras abstract letabe a pi algebra over a fieldf we study the asymptotic behavior of the sequence of codimensionscn a ofa we show that ifais finitely generated overftheninv a limn c n a always exists and is an integer we also obtain the following characterization of simple algebras ais finite dimensional central simple overfif and only ifinv a dim a

noncommutative invariant theory of symplectic and orthogonal groups abstract we present a method for computing the hilbert series of the algebra of invariants of the complex symplectic and orthogonal groups acting on graded noncommutative algebras with homogeneous components which are polynomial modules of the general linear group we apply our method to compute the hilbert series for different actions of the symplectic and orthogonal groups on the relatively free algebras of the varieties of associative algebras generated respectively by the grassmann algebra and the algebra of 2 2 upper triangular matrices these two varieties are remarkable with the property that they are the only minimal varieties of exponent 2

one sided and two sided tolerance intervals in general mixed and random effects models using small sample asymptotics the computation of tolerance intervals in mixed and random effects models has not been satisfactorily addressed in a general setting when the data are unbalanced and or when covariates are present this article derives satisfactory one sided and two sided tolerance intervals in such a general scenario by applying small sample asymptotic procedures in the case of one sided tolerance limits the problem reduces to the interval estimation of a percentile and accurate confidence limits are derived using small sample asymptotics in the case of a two sided tolerance interval the problem does not reduce to an interval estimation problem however it is possible to derive an approximate margin of error statistic that is an upper confidence limit for a linear combination of the variance components for the latter problem small sample asymptotic procedures can once again be used to arrive at an accurate upper confidence limit in the article balanced and unbalanced data situations are treated separately and

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

semi centralizing maps of generalized matrix algebras abstract the present article is a continuation of our former work xiao and wei 2010 35 to some extent motivated by bresar s and cheung s wonderful ideas we will study semi centralizing maps of generalized matrix algebras and describe its general form by routine and complicated computations skew commuting maps and semi centralizing maps of generalized matrix algebras are specially considered we prove that any skew commuting map on a class of generalized matrix algebras is zero and that any semi centralizing derivation on a generalized matrix algebra is zero these results not only give new perspectives to the work of bresar 2004 6 but also extend the main results of cheung 2001 13 a number of applications related to semi centralizing maps are given

graded polynomial identities as identities of universal algebras abstract let a and b be finite dimensional simple algebras with arbitrary signature over an algebraically closed field suppose a and b are graded by a semigroup s so that the graded identical relations of a are the same as those of b then a is isomorphic to b as an s graded algebra

minimal algebras with respect to their exponent abstract given an m tuple a 1 a m of finite dimensional simple algebras we introduce a block triangular matrix algebra with involution denoted as ut a 1 a m where each a i can be embedded as algebra we describe the t ideal of r ut a 1 a m in terms of the ideals t a i and prove that any algebra with involution which is minimal with respect to its exponent is pi equivalent to r for a suitable choice of a 1 a m moreover we show that if m 1 or a i f for all i then r itself is a minimal algebra the assumption for the base field f is characteristic zero

on the factorability of polynomial identities of upper block triangular matrix algebras graded by cyclic groups abstract let f be an algebraically closed field of characteristic zero and g be an arbitrary finite cyclic group in this paper given an m tuple a 1 a m of finite dimensional g simple algebras we focus on the study of the factorability of the t g ideals id g u t a 1 a m of the g graded upper block triangular matrix algebras u t a 1 a m endowed with elementary g gradings induced by some maps when g is a cyclic p group we prove that the factorability of the ideal id g u t a 1 a m is equivalent to the g regularity of all except for at most one the g simple components a 1 a m as well to the existence of a unique isomorphism class of admissible elementary g gradings for u t a 1 a m moreover we present some necessary and sufficient conditions to the factorability of id g u t a 1 a 2 even in case g is not a p group with some stronger assumptions on the gradings of the algebras a 1 and a 2

nonparametric mixed effects models for unequally sampled noisy curves we propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients the method is applicable when the individual curves are sampled at variable and irregularly spaced points this produces a low rank low frequency approximation to the covariance structure which can be estimated naturally by the em algorithm smooth curves for individual trajectories are constructed as best linear unbiased predictor blup estimates combining data from that individual and the entire collection this framework leads naturally to methods for examining the effects of covariates on the shapes of the curves we use model selection techniques akaike information criterion aic bayesian information criterion bic and cross validation to select the number of breakpoints for the spline approximation we believe that the methodology we propose provides a simple flexible and computationally efficient means of functional data analysis