trace like functionals on the double of the taft hopf algebra abstract the cocommutative elements of the dual of the double d h which are the trace like functionals on d h of the taft hopf algebra h over a field k are studied in detail the subalgebra of cocommutative elements of d h is isomorphic to the center of d h trace like functionals on d h determine regular isotopy invariants of oriented knots and links specific calculations made here suggest that further study of these invariants is definitely warranted

oriented quantum algebras and invariants of knots and links abstract in our previous work oriented quantum algebras were motivated and introduced in a very natural categorical setting within the context of knots and links some examples were discussed and a rudimentary theory of oriented quantum algebras was sketched invariants of knots and links can be computed from oriented quantum algebras here we continue the study of oriented quantum algebras we view them from a more algebraic perspective and develop a more detailed theory for them and their associated invariants we study a class of examples associated with the homfly polynomial in depth

approximations of marginal tail probabilities and inference for scalar parameters summary in many situations inference for a scalar parameter in the presence of nuisance parameters requires integration of either a joint density of pivotal quantities or a joint posterior density for such inference accurate approximations of marginal tail probabilities are useful to avoid high dimensional integrals two tail probability approximations are developed in this paper numerical results given for conditional inference in location scale and linear regression models show the approximations to be generally accurate even for small sample sizes

some interrelations between hopf algebras and their duals abstract in this paper we study certain interrelations between subsets of hopf algebras h and their duals which stem from various morphisms t defined on h we define and study t cocommutative elements cocommutative elements generators of h as an h module and invariants under various actions and coactions are all examples an important role is played by nakayama automorphisms these ideas are applied to co quasitriangular hopf algebras in particular when they are factorizable then the drinfeld element gives rise to a nakayama automorphism and to a special element in the dual explicit calculations are carried out for the drinfeld double

invariants of 3 manifolds and projective representations of mapping class groups via quantum groups at roots of unity an example of a finite dimensional factorizable ribbon hopf algebra is given by a quotienth u q g of the quantized universal enveloping algebrau q g at a root of unityq of odd degree the mapping class groupm g 1 of a surface of genusg with one hole projectively acts by automorphisms in theh moduleh g ifh is endowed with the coadjointh module structure there exists a projective representation of the mapping class groupm g n of a surface of genusg withn holes labeled by finite dimensionalh modulesx 1 x n in the vector space hom h x 1 x n h g an invariant of closed oriented 3 manifolds is constructed modifications of these constructions for a class of ribbon hopf algebras satisfying weaker conditions than factorizability including most ofu q g at roots of unityq of even degree are described

structure constants related to symmetric hopf algebras abstract let k be an algebraically closed field of characteristic 0 in this paper we continue our study of structure constants for semisimple hopf algebras h whose character algebra is commutative and for non semisimple factorizable ribbon hopf algebras this is done from the point of view of symmetric algebras such as group algebras in particular we consider general fusion rules which are structure constants associated to products of irreducible characters and structure constants associated to generalizations of class sums and conjugacy classes our methods are reminiscent on one hand of the methods employed when analyzing tilting modules for certain quantum groups and on the other hand of splitting modules for certain drinfeld doubles the family of irreducible characters is divided in two according to the vanishing of their quantum dimension the fusion rules on the character algebra are computed with respect to this division

on two invariants of three manifolds from hopf algebras abstract we prove a 20 year old conjecture concerning two quantum invariants of three manifolds that are constructed from finite dimensional hopf algebras namely the kuperberg invariant and the hennings kauffman radford invariant the two invariants can be viewed as a non semisimple generalization of the turaev viro barrett westbury tvbw invariant and the witten reshetikhin turaev wrt invariant respectively by a classical result relating tvbw and wrt it follows that the kuperberg invariant for a semisimple hopf algebra is equal to the hennings kauffman radford invariant for the drinfeld double of the hopf algebra however whether the relation holds for non semisimple hopf algebras has remained open partly because the introduction of framings in this case makes the kuperberg invariant significantly more complicated to handle we give an affirmative answer to this question an important ingredient in the proof involves using a special heegaard diagram in which one family of circles gives the surgery link of the three manifold represented by the heegaard diagram

assessing the accuracy of normal approximations abstract the widespread applicability and use of normal approximations creates a need for methods for assessing their accuracy in an operational fashion in this article two new methods are proposed and exemplified these new methods are based on a comparison of the level curves of an exact likelihood with the level curves of the usual normal approximation to it and on a comparison of selected line integrals of an exact density and a normal approximation to it the operational usefulness of these methods is compared with the operational usefulness of two well known existing approaches to assessing the accuracy of approximations namely convergence rates and the curvature methods of bates and watts 1980 as an example the second method is applied to the lee geisser 1972 1975 approximation to the predictive distribution of dental measurements on girls at the ages of 8 10 12 and 14 years in this application the method shows that the 50 central predictive probability region has actual predicti

bayesian marginal inference abstract a method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite possibly tedious numerical integrations are replaced by conditional maximizations which are shown to be quite accurate in a number of special cases there are similarities with the profile likelihood ideas originated by kalbfleisch and sprott 1970 and the method is contrasted with a laplacian approximation recommended by kass tierney and kadane 1988 in press referred to here as the ktk procedure the methods are used to approximate the marginal posterior densities of the log linear interaction effects and an overall measure of association in a two way contingency table snee s 1974 hair eye color data are reanalyzed and adjustments are proposed to goodman s 1964 analysis for the full rank interaction model another application concerns marginaliz

diagnostic plots for improved parameterization in bayesian inference summary a major problem with the bayesian analysis of statistical models is that the computation of posterior and predictive summaries typically requires the numerical evaluation of complicated multivariate integrals the accuracy and efficiency of these computations are usually sensitive to the choice of parameterization for the statistical model this paper describes a graphical method which can be used both for assessing a proposed parameterization and choosing a new improved parameterization

development of a high resolution scheme for a multi dimensional advection diffusion equation in this article we present a composite scheme to solve the scalar transport equation in a two dimensional space the aim of this study is to accurately resolve sharp profiles in the flow the theory of the m matrix serves as the theoretical foundation for achieving this goal attempts to extend the approach to resolve discontinuities in all cases motivate the development of the composite scheme for this study a conditionally monotonic legendre polynomial finite element model is used together with an unconditionally monotonic scheme computational evidence reveals that the composite model improves stability while it maintains accuracy the application scope is thus greatly extended

ribbon transformations integrals and triangular decompositions abstract we study the theory of integrals in yetter drinfel d hopf algebras and use the results to determine the integrals of hopf algebras with triangular decomposition

modular invariant frobenius algebras from ribbon hopf algebra automorphisms abstract for any finite dimensional factorizable ribbon hopf algebra h and any ribbon automorphism of h we establish the existence of the following structure an h bimodule f and a bimodule morphism z from lyubashenko s hopf algebra object k for the bimodule category to f this morphism is invariant under the natural action of the mapping class group of the one punctured torus on the space of bimodule morphisms from k to f we further show that the bimodule f can be endowed with a natural structure of a commutative symmetric frobenius algebra in the monoidal category of h bimodules and that it is a special frobenius algebra iff h is semisimple the bimodules k and f can both be characterized as coends of suitable bifunctors the morphism z is obtained by applying a monodromy operation to the coproduct of f a similar construction for the product of f exists as well our results are motivated by the quest to understand the bulk state space and the bulk partition function in two dimensional conformal field theories with chiral algebras that are not necessarily semisimple

a mixed effects model for overdispersed count data in animal breeding count data models are developed for animal breeding applications to account for more variability than in a poisson mixed effects model a gamma distribution is assigned to poisson parameters thereby leading to a negative binomial model the natural log of the expected value of the poisson parameter is expressed as a linear function of fixed and random polygenic effects the negative binomial and poisson mixed models were compared in two simulations in the first marginal maximum likelihood mml estimates of genetic variances obtained under a poisson sire model psm and under a poisson animal model pam accounting for half sib relationships were different contrary to what occurs in a gaussian mixed linear model mml estimates of genetic variance under a negative binomial sire model were less biased than estimates under a psm and had a slightly smaller mean squared error mse the second simulation compared animal models in which the variance of the residuals was larger than the genetic variance empirical relative bias and mse of mml estimates of genetic variance were larger under a pam that ignored the residuals than under a negative binomial animal model differences in performance widened as genetic variance increased an application to the analysis of number of artificial inseminations until conception in dairy heifers is presented to illustrate potential differences in genetic variance estimates under the two animal models

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

on oriented quantum algebras derived from representations of the quantum double of a finite dimensional hopf algebra abstract let h be a finite dimensional hopf algebra over a field k we study the simple left modules m of the drinfel d double d h and characterize them when h is graded with commutative cocommutative bottom term in the special case when h is a taft hopf algebra or a close relative we calculate the character of m and give an explicit description of oriented quantum algebra structures on end m related to a very natural oriented quantum algebra structure on d h the r matrices associated with end m are spin preserving

simple and accurate scheme for nonlinear convection diffusion equation 717 abstract a simple nonlinear scheme for iterative solution of nonlinear convection diffusion equation is described the scheme is tested by solutions of three nonlinear steady state model equations and linear nonstationary transport equation the feature of the scheme is transition from a second order accuracy on coarse grids to a first order on fine grids

on parameter transformations and interval estimation summary parameterizations which reduce the asymptotic bias and skewness of various pivotal quantities arising in large sample theory are discussed for models depending on an unknown scalar parameter transformation formulae by which such parameterizations can be obtained are derived and these formulae extend those for one dimensional curved exponential families given by hougaard 1982 to assess the accuracy of normal approximations to the distributions of the pivots their second order properties are considered and comparisons with the signed square root of the likelihood ratio statistic are drawn

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

characters and a verlinde type formula for symmetric hopf algebras abstract we study certain aspects of finite dimensional non semisimple symmetric hopf algebras h and their duals h we focus on the set i h of characters of projective h modules which is an ideal of the algebra of cocommutative elements of h this ideal corresponds via a symmetrizing form to the projective center higman ideal of h which turns out to be h where is an integral of h and is the left adjoint action of h on itself we describe h via primitive and central primitive idempotents of h we also show that it is stable under the quantum fourier transform our best results are obtained when h is a factorizable ribbon hopf algebra over an algebraically closed field of characteristic 0 in this case h is also the image of i h under a translated drinfel d map we use this fact to prove the existence of a steinberg like character the above ingredients are used to prove a verlinde type formula for h

on a parameterized family of twist quantum coalgebras and the bracket polynomial quantum coalgebras over a field k are structures that produce regular isotopy invariants of 1 1 tangles and twist quantum coalgebras over k are structures that produce regular isotopy invariants of knots these structures are introduced and studied in 9 in 6 and 8 certain families of quantum coalgebras and their resulting invariants of 1 1 tangles are examined in detail in this paper we use the simple coalgebra c k the dual of the algebra mn k of n x n matrices over k as a starting point for constructing twist quantum coalgebras among the twist quantum coalgebras we construct is a parameterized family related to the jones polynomial in an interesting way the jones polynomial can be computed by the normalized bracket polynomial 5 theorem 5 2 the bracket polynomial for knots in turn can be calculated from a quantum algebra structure on m2 c which is described in 5 p 580 the dual of this quantum algebra is a certain twist quantum coalgebra structure on c2 c which is discussed in 9 sect 8 thus the jones polynomial for knots can be computed from a twist quantum coalgebra structure on c2 c